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On the dimension of the subfield subcodes of 1-point Hermitian codes

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  • Subfield subcodes of algebraic-geometric codes are good candidates for the use in post-quantum cryptosystems, provided their true parameters such as dimension and minimum distance can be determined. In this paper we present new values of the true dimension of subfield subcodes of $ 1 $–point Hermitian codes, including the case when the subfield is not binary.

    Mathematics Subject Classification: Primary: 11T71, 14G50; Secondary: 94B27.

    Citation:

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  • Table 1.  Parameters of $ C_{8,2}(s) $ for $ s\in\{256,\ldots,511\} $

    $ s $ $ \dim C_{8,2}(s) $ $ \dim \mathcal{H}(64,s) $ $ s $ $ \dim C_{8,2}(s) $ $ \dim \mathcal{H}(64,s) $
    256 7 229 456 206 429
    288 13 261 457 212 430
    292 19 265 458 218 431
    320 25 293 460 224 433
    324 28 297 462 226 435
    328 34 301 464 232 437
    336 36 309 466 238 439
    352 42 325 468 244 441
    356 48 329 470 250 443
    360 54 333 472 256 445
    364 60 337 473 262 446
    368 66 341 474 268 447
    376 72 349 475 274 448
    378 74 351 480 280 453
    384 80 357 482 286 455
    392 86 365 484 292 457
    400 92 373 486 295 459
    402 98 375 488 301 461
    408 104 381 489 307 462
    410 110 383 490 313 463
    416 116 389 491 319 464
    418 122 391 492 325 465
    420 128 393 493 331 466
    424 134 397 496 337 469
    428 140 401 498 343 471
    432 146 405 500 349 473
    434 152 407 502 355 475
    436 158 409 504 361 477
    438 164 411 505 367 478
    440 170 413 506 373 479
    442 176 415 507 379 480
    444 182 417 508 385 481
    448 188 421 509 391 482
    450 194 423 510 397 483
    452 200 425 511 403 484
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  • [1] D. Augot, M. Barbier and A. Couvreur, List-decoding of binary Goppa codes up to the binary Johnson bound, 2011 IEEE Information Theory Workshop, (2011), 229–233. doi: 10.1109/ITW.2011.6089384.
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