1############################################################################# 2## 3#A refs.g GUAVA library Reinald Baart 4#A & Jasper Cramwinckel 5#A & Erik Roijackers 6## 7## This file contains a record, which fields are references used in the 8## tables. 9## 10#Y Copyright (C) 1994, Vakgroep Algemene Wiskunde, T.U. Delft, Nederland 11## 12#H CJ, 17 May 2006 13#H Updated lower- and upper-bounds of minimum distance for GF(2), 14#H GF(3) and GF(4) codes. (Brouwer's table as of 11 May 2006) 15#H 16#H $Log: refs.g,v $ 17#H Revision 1.1.1.1 1998/03/19 17:31:43 lea 18#H Initial version of GUAVA for GAP4. Development still under way. 19#H Lea Ruscio 19/3/98 20#H 21#H 22#H Revision 1.2 1997/01/20 15:34:33 werner 23#H Upgrade from Guava 1.2 to Guava 1.3 for GAP release 3.4.4. 24#H 25#H Revision 1.2 1994/11/10 14:34:24 rbaart 26#H Removed spaces 27#H 28#H Revision 1.1 1994/11/10 14:29:23 rbaart 29#H Initial revision 30#H 31## 32GUAVA_REF_LIST := rec( 33ask := ["%T this reference is unknown, for more info", 34 "%T contact A.E. Brouwer (aeb@cwi.nl)"], 35 36CLC := ["%A C.L. Chen", 37 "%T On a (145,32) binary cyclic code", 38 "%J IEEE Trans. Inform. Theory", 39 "%V 45", 40 "%P 2546-2547", 41 "%D Nov. 1999"], 42 43cy := ["%R Cyclic Code"], 44 45cyx := ["%R Construction X applied to cyclic Code"], 46 47XBZ := ["%R extended Blokh-Zyablov concatenated code"], 48 49XB := ["%R extended Blokh-Zyablov concatenated code"], 50 51X := ["%A N.J. Sloane, S.M. Reddy & C.L. Chen", 52 "%T New binary codes", 53 "%J IEEE Trans. Inform. Theory", 54 "%V IT-18", 55 "%P 503-510", 56 "%D Jul. 1972", 57 "%O Construction X"], 58 59XX := ["%A W.O. Alltop", 60 "%T A method of extending binary linear codes", 61 "%J IEEE Trans. Inform. Theory", 62 "%V 30", 63 "%P 871-872", 64 "%D Nov. 1984", 65 "%O Construction XX"], 66 67FP := ["%A A.B. Fontaine & W.W. Peterson", 68 "%T Group code equivalence and optimum codes", 69 "%J IRE Trans. Inform. Theory (Spec. Suppl.)", 70 "%V IT-5", 71 "%P 60-70", 72 "%D May 1959"], 73 74QR := ["%R A quadratic residue code"], 75 76Wa := ["%A T.J. Wagner", 77 "%T A remark concerning the minimum distance of binary group codes", 78 "%J IEEE Trans. Inform. Theory", 79 "%V IT-11", 80 "%P 458", 81 "%D July 1965"], 82 83HP := ["%A A.A. Hashim & V.S. Pozdniakov", 84 "%T Computerized search for linear binary codes", 85 "%J Electronics Letters", 86 "%V 12", 87 "%P 350-351", 88 "%D July 1976"], 89 90YH1 := ["%A �yvind Ytrehus & Tor Helleseth", 91 "%T There is no binary [25,8,10] code", 92 "%J IEEE Trans. Inform. Theory", 93 "%V 36", 94 "%P 695-696", 95 "%D May 1990"], 96 97Si := ["%A J. Simonis", 98 "%T Binary even [25,15,6] codes do not exist", 99 "%J IEEE Trans. Inform. Theory", 100 "%V IT-33", 101 "%P 151-153", 102 "%D Jan. 1987"], 103 104Pi2 := ["%A P. Piret", 105 "%T Good linear codes of lengths 27 and 28", 106 "%J IEEE Trans. Inform. Theory", 107 "%V IT-26", 108 "%P 227", 109 "%D Mar. 1980"], 110 111Ch0 := ["%A C.L. Chen", 112 "%T Construction of some binary linear codes of minimum distance five", 113 "%J IEEE Trans. Inform. Theory", 114 "%V 37", 115 "%P 1429", 116 "%D Sep 1991"], 117 118Pu2 := ["%A C.L.M. van Pul, [26,13,8] does not exist", 119 "%R priv. comm", 120 "%D 1985"], 121 122Ka := ["%A M. Karlin", 123 "%T New binary coding results by circulants", 124 "%J IEEE Trans. Inform. Theory", 125 "%V IT-15", 126 "%P 81-92", 127 "%D Jan. 1969"], 128 129DM := ["%A S.M. Dodunekov & N.L. Manev", 130 "%T An improvement of the Griesmer bound for some small minimum distances", 131 "%J Discr. Appl. Math.", 132 "%V 12", 133 "%P 103-114", 134 "%D Oct. 1985"], 135 136BM := ["%A L.D. Baumert & R.J. McEliece", 137 "%T A note on the Griesmer bound", 138 "%J IEEE Trans. Inform. Theory", 139 "%V IT-19", 140 "%P 134-135", 141 "%D Jan. 1973"], 142 143XBC := ["%R Extended BCH code"], 144 145Ja := ["%A D.B. Jaffe", 146 "%T Binary linear codes: new results on nonexistence", 147 "%D 1996", 148 "%O http://www.math.unl.edu/~djaffe/codes/code.ps.gz"], 149 150CS := ["%A Y. Cheng & N.J.A. Sloane", 151 "%T Codes from symmetry groups", 152 "%J SIAM J. Discrete Math.", 153 "%V 2", 154 "%P 28-37", 155 "%D 1989"], 156 157vT3 := ["%A H.C.A. van Tilborg", 158 "%T The smallest length of binary 7-dimensional linear codes with prescribed minimum distance", 159 "%J Discr. Math.", 160 "%V 33", 161 "%P 197-207", 162 "%D 1981"], 163 164HY2 := ["%A T. Helleseth & �. Ytrehus", 165 "%T How to find a [33,8,14]-code", 166 "%R Report in Informatics (preliminary version), Dept. of Informatics, Univ. of Bergen, Norway", 167 "%D Nov. 1989"], 168 169He := ["%A P.W. Heijnen", 170 "%T Er bestaat geen binaire [33,9,13] code", 171 "%R Afstudeerverslag, T.U. Delft", 172 "%D Oct. 1993"], 173 174DHM := ["%A S.M. Dodunekov, T. Helleseth, N. Manev & �. Ytrehus", 175 "%T New bounds on binary linear codes of dimension eight", 176 "%J IEEE Trans. Inform. Theory", 177 "%V IT-33", 178 "%P 917-919", 179 "%D Nov. 1987"], 180 181Pi := ["%A P. Piret", 182 "%T Good block codes derived from cyclic codes", 183 "%J Electronics Letters", 184 "%V 10", 185 "%P 391-392", 186 "%D Sep. 1974"], 187 188BoV := ["%A I.G. Bouyukliev & Z.G. Varbanov", 189 "%T Some results for linear binary codes with minimum distance 5 and 6", 190 "%R email", 191 "%D Oct. 2004"], 192 193Mo := ["%A M. Morii", 194 "%R email comm", 195 "%D Sept. 1993"], 196 197BE := ["%A J. Bierbrauer & Y. Edel", 198 "%T New code parameters from Reed-Solomon subfield subcodes", 199 "%J IEEE Trans. Inf. Th.", 200 "%V 43", 201 "%P 953-968", 202 "%D 1997"], 203 204FB := ["%A P. Farkas & K. Br�hl", 205 "%T Three best binary linear block codes of minimum distance fifteen", 206 "%J IEEE Trans. Inf. Th.", 207 "%V 40", 208 "%P 949-951", 209 "%D 1994"], 210 211Bou := ["%A I. Boukliev", 212 "%T Some new bounds on minimum length for quaternary codes of dimension five", 213 "%R preprint", 214 "%D July 1994"], 215 216RR := ["%A V.V. Rao & S.M. Reddy", 217 "%T A (48,31,8) linear code", 218 "%J IEEE Trans. Inform. Theory", 219 "%V IT-19", 220 "%P 709-711", 221 "%D Sep. 1973"], 222 223BJV := ["%A I Bouyukliev, D.B. Jaffe & V. Vavrek", 224 "%T The smallest length of eight-dimensional binary linear codes with prescribed minimum distance", 225 "%R preprint", 226 "%D 1999"], 227 228vT1 := ["%A H.C.A. van Tilborg", 229 "%T On quasi-cyclic codes with rate 1/m", 230 "%J IEEE Trans. Inform. Theory", 231 "%V IT-24", 232 "%P 628-630", 233 "%D Sep. 1978"], 234 235BZ := ["%A E. L. Blokh & V. V. Zyablov", 236 "%T Coding of generalized concatenated codes", 237 "%J Probl. Inform. Transm.", 238 "%V 10", 239 "%P 218-222", 240 "%D 1974"], 241 242Bo0 := ["%A I Boukliev", 243 "%R private comm", 244 "%D 1995-1997"], 245 246Bel := ["%R Belov"], 247 248Gu9 := ["%A T. A. Gulliver", 249 "%R personal communications", 250 "%D 1993-1998"], 251 252DJ := ["%A R. Dougherty & H. Janwa", 253 "%T Covering radius computations for binary cyclic codes", 254 "%J Math. Comput.", 255 "%V 57", 256 "%P 415-434", 257 "%D July 1991"], 258 259GB5 := ["%A T. A. Gulliver & V. K. Bhargava", 260 "%T New optimal binary linear codes of dimensions 9 and 10", 261 "%J IEEE Trans. Inform. Theory", 262 "%V 43", 263 "%P 314-316", 264 "%D 1997"], 265 266GG := ["%A B. Groneick & S. Grosse", 267 "%T New binary codes", 268 "%J IEEE Trans. Inform. Theory", 269 "%V 40", 270 "%P 510-512", 271 "%D 1994"], 272 273EB3 := ["%A Y. Edel & J. Bierbrauer", 274 "%T Inverting Construction Y1", 275 "%R preprint", 276 "%D 1997"], 277 278B2x := ["%A See A.E. Brouwer & T. Verhoeff", 279 "%T An updated table of minimum-distance bounds for binary linear codes", 280 "%J IEEE Trans. Inform. Th.", 281 "%V 39", 282 "%P 662-677", 283 "%D 1993"], 284 285Pu := ["%A C.L.M. van Pul", 286 "%T On bounds on codes", 287 "%R Master's Thesis, Dept. of Math. and Comp. Sc., Eindhoven Univ. of Techn., The Netherlands", 288 "%D Aug. 1982"], 289 290LC := ["%A M. Loeloeian & J. Conan", 291 "%T A [55,16,19] binary Goppa code", 292 "%J IEEE Trans. Inform. Theory", 293 "%V IT-30", 294 "%P 773", 295 "%D Sep. 1984"], 296 297Bro := ["%A A.E. Brouwer", 298 "%T The linear programming bound for binary linear codes", 299 "%J IEEE Trans. Inform. Th.", 300 "%V 39", 301 "%P 677-680", 302 "%D 1993"], 303 304vT4 := ["%A H.C.A. van Tilborg", 305 "%T A proof of the nonexistence of a binary (55,7,26) code", 306 "%R TH-Report 79-WSK-09, Techn. Hogeschool Eindhoven", 307 "%D Nov. 1979"], 308 309Ja2 := ["%A D. Jaffe", 310 "%R email", 311 "%D 970828, 970907, 970923, 971111, 980112, 980323"], 312 313MoY := ["%A M. Morii & T. Yoshimura", 314 "%R email comm", 315 "%D Nov 1993-Jan 1994"], 316 317BCH := ["%A T. Kasami & N. Tokura", 318 "%T Some remarks on BCH bounds and minimum weights of binary primitive BCH codes", 319 "%J IEEE Trans. Inform. Theory", 320 "%V IT-15", 321 "%P 408-413", 322 "%D May 1969"], 323 324SRC := ["%A N.J.A. Sloane, S.M. Reddy & C.L. Chen", 325 "%T New binary codes", 326 "%J IEEE Trans. Inform. Theory", 327 "%V IT-18", 328 "%P 503-510", 329 "%D July 1972"], 330 331We := ["%A S. Weijs", 332 "%T A computer search for quasi-cyclic codes", 333 "%R afstudeerverslag (M.Sc. Thesis), Techn. Univ. Eindhoven", 334 "%D June 1997", 335 "%O See also P. Heijnen, H. van Tilborg, T. Verhoeff & S. Weijs, Some new binary, quasi-cyclic codes, IEEE Trans. Inf. Th., to appear"], 336 337Ch := ["%A Y. Cheng", 338 "%T New linear codes constructed by concatenating, extending, and shortening methods", 339 "%J IEEE Trans. Inform. Theory", 340 "%V IT-33", 341 "%P 719-721", 342 "%D Sept. 1987"], 343 344CDJ := ["%A Huy T. Cao, Randall L. Dougherty & Heeralal Janwa", 345 "%T A [55,16,19] binary Goppa code and related codes, having large minimum distance", 346 "%J IEEE Trans. Inform. Theory", 347 "%V 37", 348 "%P 1432", 349 "%D Sep. 1991"], 350 351Hel := ["%A T. Helleseth", 352 "%T A characterization of codes meeting the Griesmer bound", 353 "%J Inform. & Control", 354 "%V 50", 355 "%P 128-159", 356 "%D 1981"], 357 358Sa := ["%A Amir Said", 359 "%R private comm", 360 "%D 910510 and 911121"], 361 362GW2 := ["%A M. Grassl & G. White", 363 "%T New Codes from Chains of Quasi-cyclic Codes", 364 "%R ISIT", 365 "%D 2005"], 366 367GG1 := ["%A B. Groneick & S. Grosse", 368 "%R priv. comm. and comm. via W. Scharlau", 369 "%D 1992-1993"], 370 371CZ := ["%A Chen Zhi", 372 "%T Six new binary quasi-cyclic codes", 373 "%J IEEE Trans. Inf. Theory", 374 "%V 40", 375 "%P 1666-1667", 376 "%D 1994"], 377 378GB0 := ["%A T. Aaron Gulliver & Vijay K. Bhargava", 379 "%T Nine good rate (m-1)/pm quasi-cyclic codes", 380 "%J IEEE Trans. Inform. Th.", 381 "%V 38", 382 "%P 1366-1369", 383 "%D July 1991"], 384 385To := ["%A L.M.G.M. Tolhuizen", 386 "%T On the optimal use and the construction of linear block codes", 387 "%R Master's Thesis, Dept. of Math. and Comp. Sc., Eindhoven Univ. of Techn., The Netherlands", 388 "%D Nov. 1986"], 389 390To2 := ["%A Ludo M.G.M. Tolhuizen", 391 "%T Two new binary codes obtained by shortening a generalized concatenated code", 392 "%J IEEE Trans. Inform. Theory", 393 "%V 37", 394 "%P 1705", 395 "%D Nov. 1991"], 396 397ZL := ["%A V.A. Zinoviev & S.N. Litsyn", 398 "%T Methods of code lengthening", 399 "%J Problemy Peredachi Informatsii", 400 "%V 18", 401 "%P 29-42", 402 "%D Oct-Dec 1982", 403 "%O (English translation: pp. 244-254)"], 404 405EB2 := ["%A Y. Edel & J. Bierbrauer", 406 "%T Twisted BCH codes", 407 "%J J. of Combinatorial Designs", 408 "%V 5", 409 "%P 377-389", 410 "%D 1997"], 411 412BEx := ["%A J. Bierbrauer & Y. Edel", 413 "%T New code parameters from Reed-Solomon subfield subcodes", 414 "%J IEEE Trans. Inf. Th.", 415 "%V 43", 416 "%P 953-968", 417 "%D 1997"], 418 419JS := ["%A D. Jaffe & J. Simonis", 420 "%R email", 421 "%D 970722, 980217"], 422 423GB1 := ["%A T. A. Gulliver & V. K. Bhargava", 424 "%T Two new rate $2/p$ binary quasi-cyclic codes", 425 "%J IEEE Trans. Inf. Theory", 426 "%V 40", 427 "%P 1667-1668", 428 "%D 1994"], 429 430BET := ["%A J. Bierbrauer, Y. Edel & L. Tolhuizen", 431 "%T New codes via the lengthening of BCH codes with UEP codes", 432 "%R preprint", 433 "%D 1997"], 434 435Hg := ["%A H.J. Helgert", 436 "%T Alternant codes", 437 "%J Inform. Contr.", 438 "%V 26", 439 "%P 369-380", 440 "%D Dec. 1974"], 441 442BDH := ["%A I. Boukliev, S. M. Dodunekov, T. Helleseth & �. Ytrehus", 443 "%T On the [162,8,80;2] codes", 444 "%R preprint", 445 "%D 1996"], 446 447HS := ["%A H.J. Helgert & R.D. Stinaff", 448 "%T Shortened BCH codes", 449 "%J IEEE Trans. Inform. Theory", 450 "%V IT-19", 451 "%P 818-820", 452 "%D Nov. 1973"], 453 454BK := ["%A Detlef Berntzen & Peter Kemper", 455 "%R email", 456 "%D Feb. 1993"], 457 458LP := ["%R Follows from the linear programming bound"], 459 460DMa := ["%A S. M. Dodunekov & N. L. Manev", 461 "%T An improvement of Greismer bound for some classes of distances", 462 "%J Probl. Peredachi Informatsii", 463 "%V 23", 464 "%P 47-56", 465 "%D 1987", 466 "%O (Russian); English transl. in Problems of Inform. Transm. 23 (1987) 38-46"], 467 468Jo2 := ["%A S.M. Johnson", 469 "%T On upper bounds for unrestricted binary error-correcting codes", 470 "%J IEEE Trans. Inform. Theory", 471 "%V IT-17", 472 "%P 466-478", 473 "%D July 1971"], 474 475DaH := ["%A Rumen Daskalov & Plamen Hristov", 476 "%T New One-Generator Quasi-Cyclic Codes over GF(7)", 477 "%R preprint", 478 "%D Oct 2001", 479 "%O R. Daskalov & P Hristov, New One-Generator Quasi-Twisted Codes over GF(5), (preprint) Oct. 2001. R. Daskalov & P Hristov, <i>New Quasi-Twisted Degenerate Ternary Linear Codes, preprint, Nov 2001. Email, 2002-2003"], 480 481AGP := ["%A A.O.L. Atkin, P. Gaborit, V. Pless & P Sole", 482 "%R email", 483 "%D 2001"], 484 485Roe := ["%A G. Roelofsen", 486 "%T On Goppa and generalized Srivastava codes", 487 "%R Master's Thesis, Dept. of Math. and Comp. Sc., Eindhoven Univ. of Techn., The Netherlands", 488 "%D Aug. 1982"], 489 490Joplus := ["%A A.E. Brouwer", 491 "%T The linear programming bound for binary linear codes", 492 "%J IEEE Trans. Inform. Th.", 493 "%V 39", 494 "%P 677-680", 495 "%D 1993"], 496 497Gp := ["%A V. D. Goppa", 498 "%T A new class of linear error-correcting codes", 499 "%J Problems of Info. Transmission", 500 "%V 6", 501 "%P 207-212", 502 "%D 1970"], 503 504GB := ["%A T. Aaron Gulliver & Vijay K. Bhargava", 505 "%T Some best rate 1/p and rate (p-1)/p systematic quasi-cyclic codes", 506 "%J IEEE Trans. Inform. Theory", 507 "%V 37", 508 "%P 552-555", 509 "%D May 1991"], 510 511QC := ["%A A.E. Brouwer & T. Verhoeff", 512 "%T An updated table of minimum-distance bounds for binary linear codes", 513 "%J IEEE Trans. Inform. Theory", 514 "%V 39", 515 "%P 662-677", 516 "%D 1993"], 517 518MMT := ["%A Hideaki TANAKA, Masami MOHRI, Masakatu MORII", 519 "%R email, comm", 520 "%D Feb 2005"], 521 522EB1 := ["%A Y. Edel & J. Bierbrauer", 523 "%T Some codes related to BCH codes of low dimension", 524 "%R preprint", 525 "%D 1995"], 526 527BJK := ["%A Irina E. Bocharova, Rolf Johannesson, Boris D. Kudryashov & Per St�hl", 528 "%T Tailbiting Codes: Bounds and Search Results", 529 "%O IEEE, to appear"], 530 531BHJ := ["%A I. E. Bocharova, M. Handlery, R. Johannesson & B. D. Kudryashov", 532 "%T Tailbiting Codes Obtained via Convolutional Codes with Large Slope", 533 "%O to be submitted to IEEE"], 534 535RS := ["%A Rains & Sloane", 536 "%T Self-dual codes", 537 "%O in: Handbook of Coding theory, Table XI, p. 274"], 538 539Dup := ["%A Scott Duplichan", 540 "%R email 000517"], 541 542Gur := ["%A Sugi Guritman", 543 "%T Restrictions on the weight distribution of linear codes", 544 "%R Thesis, Techn. Univ. Delft", 545 "%D 2000"], 546 547BE3 := ["%A J. Bierbrauer & Y. Edel", 548 "%T Extending and lengthening BCH-codes", 549 "%R preprint"], 550 551Su := ["%A Y. Sugiyama, M. Kasahara, S. Hirasawa & T. Namekawa", 552 "%T Some efficient binary codes constructed using Srivastava codes", 553 "%J IEEE Trans. Inform. Theory", 554 "%V IT-21", 555 "%P 581-582", 556 "%D Sep. 1975"], 557 558Vx := ["%R From the Varshamov-Gilbert bound together with construction X"], 559 560Jo := ["%R Follows from the Johnson bound"], 561 562GB6 := ["%A T. A. Gulliver & V. K. Bhargava", 563 "%T Improvements to the bounds on optimal binary linear codes of dimensions 11 and 12", 564 "%J Ars Combinatoria", 565 "%V 44", 566 "%P 173-181", 567 "%D 1996"], 568 569Kol := ["%A David R. Kohel", 570 "%R email", 571 "%D 1998-11-19"], 572 573Gu := ["%A T. A. Gulliver", 574 "%R personal communications", 575 "%D 1993-1998"], 576 577HvT := ["%A Tor Helleseth & Henk C.A. van Tilborg", 578 "%T The classification of all (145,7,72) binary linear codes", 579 "%R TH-Report 80-WSK-01, Techn. Hogeschool Eindhoven", 580 "%D April 1980"], 581 582TTH := ["%A C. Tjhai, M. Tomlinson, R. Horan, M. Ahmed & M. Ambroze", 583 "%T Linear codes derived from binary cyclic codes of length 151", 584 "%R preprint", 585 "%D 2005"], 586 587KSH := ["%A M. Kasahara, Y. Sugiyama, S. Hirasawa & T. Namekawa", 588 "%T A new class of binary codes constructed on the basis of BCH codes", 589 "%J IEEE Trans. Inform. Theory", 590 "%V IT-21", 591 "%P 582-585", 592 "%D Sep. 1975"], 593 594BKW := ["%A Michael Braun, Axel Kohnert & Alfred Wassermann", 595 "%T Optimal linear codes from matrix groups", 596 "%R preprint", 597 "%D Mar 2004", 598 "%O and Construction of (sometimes) Optimal Linear Codes, email, Mar 2005"], 599 600Zwa := ["%A Johannes Zwanzger", 601 "%R pers.comm", 602 "%D Dec 2005"], 603 604BG3 := ["%A M. C. Bhandari & M. S. Garg", 605 "%T A new lower bound on the minimal length of a binary linear code", 606 "%J Europ. J. Combin.", 607 "%V 17", 608 "%P 335-342", 609 "%D 1996"], 610 611Sab := ["%A Roberta E. Sabin", 612 "%R email", 613 "%D Aug. 1994"], 614 615VE := ["%R From repeated Varshamov-Edel lengthening"], 616 617MYI := ["%A M. Morii, T. Yoshimura & Y. Itoh", 618 "%R email comm", 619 "%D Feb-Mar 1995"], 620 621PD := ["%A M. Grassl", 622 "%R email", 623 "%D 2001-03-21", 624 "%O by puncturing a GG code at a word of the dual"], 625 626Rod := ["%A F. Rodier", 627 "%T On the minimum distance of the duals of 4-error correcting extended BCH codes", 628 "%R preprint", 629 "%D Oct. 1997"], 630 631Lun := ["%A Anders Lundqvist", 632 "%R pers.comm", 633 "%D 1997"], 634 635HN := ["%A R. Hill & D.E. Newton", 636 "%T Optimal ternary linear codes", 637 "%J Des. Codes Cryptogr.", 638 "%V 2", 639 "%P 137-157", 640 "%D 1992"], 641 642KP := ["%A F.R. Kschischang & S. Pasupathy", 643 "%T Some ternary and quaternary codes and associated sphere packings", 644 "%J IEEE Trans. Inform. Theory", 645 "%V 38", 646 "%P 227-246", 647 "%D 1992"], 648 649vE2 := ["%A M. van Eupen", 650 "%T Four nonexistence results for ternary linear codes", 651 "%J IEEE Trans. Inform. Theory", 652 "%V 41", 653 "%P 800-805", 654 "%D 1995"], 655 656Hi1 := ["%A R. Hill", 657 "%T On the largest size of cap in S(5,3)", 658 "%R Rend. Accad. Naz. Lincei (8) {bf 54}", 659 "%D 1973", 660 "%O 378-384"], 661 662Pel := ["%A G. Pellegrino", 663 "%T Sul massimo ordine della calotte in $S_{4,3}$", 664 "%J Matematiche", 665 "%V 25", 666 "%P 149-157", 667 "%D 1971"], 668 669Ple := ["%A V. Pless", 670 "%T On a new family of symmetry codes and related new 5-designs", 671 "%J Bull. Amer. Math. Soc.", 672 "%V 75", 673 "%P 1339-1342", 674 "%D 1969"], 675 676vE0 := ["%A M. van Eupen", 677 "%T Five new optimal ternary linear codes", 678 "%J IEEE Trans. Inform. Theory", 679 "%V 40", 680 "%P 193", 681 "%D 1994"], 682 683HHM := ["%A N. Hamada, T. Helleseth, H.M. Martinsen & �. Ytrehus", 684 "%T There is no ternary [28,6,16] code"], 685 686GuB := ["%A T. A. Gulliver", 687 "%R personal communications", 688 "%D 1993-1998"], 689 690GB4 := ["%A T. A. Gulliver & V. K. Bhargava", 691 "%T New good rate $(m-1)/pm$ ternary and quaternary cyclic codes", 692 "%J Des. Codes Cryptogr.", 693 "%V 7", 694 "%P 223-233", 695 "%D 1996"], 696 697BB := ["%A G. T. Bogdanova & I. G. Boukliev", 698 "%T New linear codes of dimension 5 over GF(3)", 699 "%R Proc. 4th Internat. Workshop on Algebraic and Combinatorial Coding Theory, Novgorod, Russia", 700 "%P 41-43", 701 "%D Sept. 1994"], 702 703Bo1 := ["%A I. Boukliev", 704 "%T A method for construction of good linear codes", 705 "%R preprint submitted to the International Workshop on Optimal Codes and Related Topics, Bulgaria, Sozopol", 706 "%D 1995"], 707 708Be := ["%A G. F. M. Beenker", 709 "%T A note on extended quadratic residue codes over GF(9) and their ternary images", 710 "%J IEEE Trans. Inform. Theory", 711 "%V 30", 712 "%P 403-405", 713 "%D 1984"], 714 715vE1 := ["%A M. van Eupen", 716 "%T Some new results for ternary linear codes of dimension $5$ and $6$", 717 "%J IEEE Trans. Inform. Theory", 718 "%V 41", 719 "%P 2048-2051", 720 "%D 1995"], 721 722BKn := ["%A Detlef Berntzen & Peter Kemper", 723 "%R email", 724 "%D Feb. 1993"], 725 726Glo := ["%A Volker von Gloeden", 727 "%T Kubische Reste Codes", 728 "%R Dipl", 729 "%D marbeit, D�sseldorf, Oktober 2002"], 730 731Gu1 := ["%A T. A. Gulliver", 732 "%T New optimal ternary linear codes of dimension 6", 733 "%J Ars Combin.", 734 "%V 40", 735 "%P 97-108", 736 "%D 1995"], 737 738HJ := ["%A R. Hill and C. Jones", 739 "%T The non-existence of ternary [47,6,29] codes"], 740 741CG := ["%A Y. Cheng & D. J. Guan", 742 "%R pers. comm"], 743 744ARS := ["%A Nuh Aydin, Dijen Ray-Chaudhuri, Irfan Siap", 745 "%R email", 746 "%D 1999-2000"], 747 748Gu2 := ["%A T. A. Gulliver", 749 "%T New optimal ternary linear codes", 750 "%J IEEE Trans. Inform. Theory", 751 "%V 41", 752 "%P 1182-1185", 753 "%D 1995"], 754 755D1 := ["%R Code found by the (u|u+v) construction"], 756 757GO := ["%A T. A. Gulliver & P. R. J. �sterg�rd", 758 "%T Improved bounds for ternary linear codes of dimension 7", 759 "%J IEEE Trans. Inform. Theory", 760 "%V 43", 761 "%P 1377-1381", 762 "%D 1997"], 763 764Ha := ["%A N. Hamada", 765 "%R pers. comm"], 766 767vEH := ["%A M. van Eupen & R. Hill", 768 "%T An optimal ternary $[69,5,45]$ code and related codes", 769 "%J Des. Codes Cryptogr.", 770 "%V 4", 771 "%P 271-282", 772 "%D 1994"], 773 774Ma := ["%A T. Maruta", 775 "%T On the nonexistence of linear codes attaining the Griesmer bound", 776 "%J Geom. Dedicata", 777 "%V 60", 778 "%P 1-7", 779 "%D 1996"], 780 781ASR := ["%A Nuh Aydin, Irfan Siap & Dijen Ray-Chaudhuri", 782 "%T New ternary quasicyclic codes with improved minimum distances", 783 "%R preprint", 784 "%D 1999"], 785 786HW1 := ["%A N. Hamada & Y. Watamori", 787 "%T The nonexistence of $[71,5,46;3]$ codes", 788 "%J J. Statist. Plann. Inf.", 789 "%V 52", 790 "%P 379-394", 791 "%D 1996"], 792 793Bo3 := ["%A I. Boukliev", 794 "%T Some new optimal ternary linear codes", 795 "%J Des. Codes Cryptogr.", 796 "%V 12", 797 "%P 5-11", 798 "%D 1997"], 799 800Da := ["%A R. N. Daskalov", 801 "%R pers. comm", 802 "%D 1992-2005"], 803 804HHY := ["%A N. Hamada, T. Helleseth & �. Ytrehus", 805 "%T On the construction of $[q^4+q^2-q,5,q^4-q^3+q^2-2q;q]$-codes meeting the Griesmer bound", 806 "%J Des. Codes Cryptogr.", 807 "%V 2", 808 "%P 225-229", 809 "%D 1992"], 810 811dB := ["%A M.A. de Boer", 812 "%T A ternary [91,9,54] code", 813 "%J preprint, 9504; A dual quaternary BCH code, 9502. Codes spanned by quadratic and Hermitian forms, IEEE Trans. Inform. Theory", 814 "%V 42", 815 "%P 1600-1604", 816 "%D 1996"], 817 818Ed2 := ["%A Y. Edel", 819 "%T Extending and lengthening BCH-codes", 820 "%R preprint", 821 "%D 9710", 822 "%O 07"], 823 824HH := ["%A N. Hamada & T. Helleseth", 825 "%T The nonexistence of some ternary linear codes and update of the bounds for n_3(6,d), 1 <= d <= 243", 826 "%R preprint", 827 "%D 1999"], 828 829LX := ["%A San Ling & Chaoping Xing", 830 "%T Polyadic Codes Revisited", 831 "%R preprint", 832 "%D 2003"], 833 834GO2 := ["%A T. A. Gulliver & P. R. J. �sterg�rd", 835 "%T Improved bounds for ternary linear codes of dimension 8", 836 "%R preprint", 837 "%D Nov. 1997"], 838 839DGM := ["%A R.N. Daskalov, T.A. Gulliver & E. Metodieva", 840 "%T New Ternary Linear Codes", 841 "%R IEEE Trans.Inf.Theory", 842 "%V 45", 843 "%P 1687-1688", 844 "%D 1999", 845 "%O no.5"], 846 847DM5 := ["%A R. N. Daskalov & E. Metodieva", 848 "%T The nonexistence of ternary [105,6,68] and [230,6,152] codes", 849 "%O Designs, Codes and Cryptography, submitted"], 850 851Ed := ["%A Y. Edel", 852 "%T Eine Verallgemeinerung von BCH-Codes", 853 "%R Ph.D. Thesis, Univ. Heidelberg", 854 "%D 1996"], 855 856Var := ["%A R.R. Varshamov", 857 "%T Problems of the general theory of linear coding", 858 "%R Ph.D. thesis, Moscow State Univ", 859 "%D 1959", 860 "%O (Russian) (from the Varshamov-Gilbert bound)"], 861 862Br2 := ["%A A. E. Brouwer", 863 "%T Linear spaces of quadrics and new good codes", 864 "%R preprint", 865 "%D 1997"], 866 867DG4 := ["%A Rumen N. Daskalov & T. Aaron Gulliver", 868 "%T New Minimum Distance Bounds for Linear Codes over Small Fields", 869 "%R preprint", 870 "%D March 2001"], 871 872Da2 := ["%A R.N. Daskalov", 873 "%T The linear programming bound for ternary linear codes", 874 "%R IEEE International Symposium on Information Theory, Trondheim", 875 "%P 423", 876 "%D 1994"], 877 878Koh := ["%A Axel Kohnert", 879 "%R email", 880 "%D 2006"], 881 882BEH := ["%A J. Barat, Y. Edel, R. Hill & L. Storme", 883 "%T On complete caps in the projective geometriesover F3, II: New improvements.", 884 "%R J. Combin. Math. and Combin. Computing 49", 885 "%P 9-31", 886 "%D 2004"], 887 888Lan := ["%A I.N. Landgev", 889 "%T Nonexistence of $[143,5,94]_3$ codes", 890 "%R Proc. Internat. Workshop on Optimal Codes and Related Topics, Sozopol, Bulgaria", 891 "%P 108-116", 892 "%D 1995"], 893 894Da9 := ["%A R. N. Daskalov", 895 "%T The sharpened linear programming bound for ternary linear codes", 896 "%R Mathematics and Education in Mathematics, Sofia", 897 "%P 158-166", 898 "%D 1995"], 899 900Lg := ["%A I.N. Landgev", 901 "%T The nonexistence of some ternary five-dimensional codes", 902 "%O Des. Codes Cryptogr., to appear"], 903 904Da0 := ["%A R. N. Daskalov", 905 "%T New Ternary Linear Codes in Dimensions 18 and 19", 906 "%R preprint", 907 "%D Oct 2001"], 908 909Da6 := ["%A R. N. Daskalov", 910 "%T Some nonexistence results for 7-dimensional ternary linear codes", 911 "%R preprint", 912 "%D 1998"], 913 914DM4 := ["%A R. N. Daskalov & E. Metodieva", 915 "%T The Linear Programming Bound for Ternary and Quaternary Linear Codes", 916 "%R preprint", 917 "%D Jan 2002"], 918 919Da5 := ["%A R. N. Daskalov", 920 "%T The non-existence of ternary linear [158,6,104] and [203,6,134] codes", 921 "%R preprint", 922 "%D 1998"], 923 924BvE := ["%A A. E. Brouwer & M. van Eupen", 925 "%T The correspondence between projective codes and 2-weight codes", 926 "%R Designs, Codes and Cryptography 11", 927 "%P 261-266", 928 "%D 1997"], 929 930GH := ["%A P.P. Greenough & R. Hill", 931 "%T Optimal linear codes over GF(4)", 932 "%J Discrete Math.", 933 "%V 125", 934 "%P 187-199", 935 "%D 1994"], 936 937MOS := ["%A F.J. MacWilliams, A.M. Odlyzko, N.J.A. Sloane & H.N. Ward", 938 "%T Self-dual codes over GF(4)", 939 "%J J. Comb. Th. (A)", 940 "%V 25", 941 "%P 288-318", 942 "%D 1978"], 943 944Liz := ["%A P. Lizak", 945 "%T Optimal quaternary linear codes", 946 "%R Ph. D. Thesis, Univ. of Salford", 947 "%D Nov. 1995"], 948 949IN := ["%A H. Itoh & M. Nakamichi", 950 "%T SbEC-DbED codes derived from experiments on a computer for semiconductor memory systems", 951 "%R Electronics and Communications in Japan", 952 "%V 66-A", 953 "%D 1983", 954 "%O No.8"], 955 956Zi := ["%A Thomas Rehfinger, N. Suresh Babu & Karl-Heinz Zimmermann", 957 "%T New Good Codes via CQuest -- A System for the Silicon Search of Linear Codes", 958 "%R Algebraic Combinatorics and Applications, A. Betten et al., eds, Springer", 959 "%P 294-306", 960 "%D 2001"], 961 962Da4 := ["%A R. N. Daskalov", 963 "%T Ten good quasicyclic 10-dimensional quaternary linear codes", 964 "%R Optimal codes and related topics, Proc. Internat. Workshop on Optimal Codes and Related Topics, Sozopol, Bulgaria", 965 "%P 45-49", 966 "%D 1995"], 967 968DG5 := ["%A Rumen N. Daskalov & T. Aaron Gulliver", 969 "%T New Quasi-Twisted Quaternary Linear Codes", 970 "%R IEEE Trans. Inf. Theory", 971 "%V 46", 972 "%P 2642-2643", 973 "%O no.7"], 974 975Du3 := ["%A I. Duursma", 976 "%R email", 977 "%D 050809"], 978 979DG := ["%A R.N. Daskalov & T.A. Gulliver", 980 "%T New good quasi-cyclic ternary and quaternary codes", 981 "%R IEEE Trans.Inf.Th.", 982 "%V 43", 983 "%P 1647-1650", 984 "%D 1997", 985 "%O no.5"], 986 987BMP := ["%A J. Bierbrauer, S. Marcugini & F. Pambianco", 988 "%T A family of highly symmetric codes", 989 "%R preprint", 990 "%D 2002"], 991 992Ayd := ["%A Nuh Aydin", 993 "%T preprint", 994 "%D 2003"], 995 996GW1 := ["%A M. Grassl & G. White", 997 "%T New Good Linear Codes by Special Puncturings", 998 "%R ISIT 2004 Chicago USA", 999 "%D June 27 - July 2 2004"], 1000 1001LMH := ["%A I. Landgev, T. Maruta, R. Hill", 1002 "%T On the nonexistence of quaternary [51,4,37] codes", 1003 "%J Finite Fields Appl.", 1004 "%V 2", 1005 "%P 96-110", 1006 "%D 1996"], 1007 1008YC := ["%A Ying Cheng", 1009 "%R pers. comm. Sloane", 1010 "%D Feb. 1993"], 1011 1012HLa := ["%A R. Hill & I. Landgev", 1013 "%T On the nonexistence of some quaternary codes", 1014 "%R Proc. IMA conf. Finite Fields and their Applications", 1015 "%D June 1994"], 1016 1017Tol := ["%A L.M.G.M. Tolhuizen", 1018 "%T Cooperating error-correcting codes and their decoding", 1019 "%R Ph.D. thesis, Eindhoven Univ. of Techn", 1020 "%D June 1996"], 1021 1022Hi := ["%A R. Hill", 1023 "%T Caps and Groups", 1024 "%J Coll. Intern. Teorie Combin. Acc. Naz. Lincei, Roma 1973, Atti dei convegni Lincei", 1025 "%V 17", 1026 "%P 389-394", 1027 "%D 1976", 1028 "%O Rome"], 1029 1030DNX := ["%A Cunsheng Ding, Harald Niederreiter & Chaoping Xing", 1031 "%T Some new codes from algebraic curves", 1032 "%R IEEE Trans. On Inform. Theory", 1033 "%V 46", 1034 "%P 2638-2642", 1035 "%D 2000"], 1036 1037Gu3 := ["%A T. A. Gulliver", 1038 "%T New optimal quaternary linear codes of dimension 5", 1039 "%J IEEE Trans. Inform. Theory", 1040 "%V 42", 1041 "%P 2260-2265", 1042 "%D 1996"], 1043 1044BDK := ["%A I. Boukliev, R. Daskalov & S. Kapralov", 1045 "%T Optimal quaternary codes of dimension five", 1046 "%J IEEE Trans. Inform. Theory", 1047 "%V 42", 1048 "%P 1228-1235", 1049 "%D 1996"], 1050 1051Da1 := ["%A R.N. Daskalov", 1052 "%T The linear programming bound for quaternary linear codes", 1053 "%R Proceedings ACCT4'94, Novgorod, Russia", 1054 "%P 74-77", 1055 "%D Sept. 11-17, 1994"], 1056 1057DM3 := ["%A R. N. Daskalov & E. Metodieva", 1058 "%T Bounds on minimum length for quaternary linear codes in dimensions six and seven", 1059 "%R Mathematics and Education in Mathematics, Sofia", 1060 "%P 156-161", 1061 "%D 1994"] 1062 1063); 1064