CCZ-invariants for all known APN functions in dimension 8

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We consider the 8180 APN functions in dimension 8 constructed by the matrix method [1] We enumerate the functions in the order in which they appear in [1].

All of these 8180 functions have one of the 21 values 11818, 12370, 13200, 13800, 13804, 13842, 13848, 14024, 14028, 14030, 14032, 14034, 14036, 14038, 14040, 14042, 14044, 14046, 14048, 14050, 15358 as their -rank. The following table lists the indices of the functions having each of the given -rank.

Γ-rank Indices
11818 1
12370 2
13200 4
13800 5
13804 6
13842 7
13848 8
14024 9
14028 20
14028 20
14028 20
14028 20
14028 20
14028 20
14028 20
4044 13, 27, 36, 37, 41, 52, 54, 57, 91, 120, 146, 163, 194, 204, 212, 248, 277, 291, 300, 307, 318, 323, 337, 367, 392, 399, 401, 417, 421, 423, 432, 436, 488
4046 19, 21, 22, 24, 25, 29, 32, 34, 38, 40, 43, 47, 48, 49, 50, 51, 53, 55, 56, 60, 61, 63, 64, 65, 66, 70, 71, 74, 75, 76, 78, 80, 85, 90, 100, 102, 104, 105, 107, 109, 110, 111, 122, 126, 129, 131, 133, 136, 142, 148, 151, 153, 160, 161, 169, 170, 173, 174, 180, 182, 183, 187, 188, 191, 193, 197, 200, 202, 211, 213, 221, 231, 232, 233, 235, 236, 239, 241, 242, 243, 244, 247, 252, 256, 257, 258, 259, 262, 263, 264,268, 279, 283, 287, 290, 292, 298, 301, 302, 303, 304, 309, 312, 314, 315, 319, 326, 328, 333, 336, 341, 343, 344, 345, 347, 349, 351, 353, 357, 358, 359, 360, 363, 365, 366, 368, 370, 371, 373, 374, 375, 376, 379, 381, 384, 385, 389, 395, 396, 400, 404, 405, 406, 409, 411, 413, 419, 426, 429, 431, 435, 438, 441, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 460, 465, 472, 475, 476, 478, 479, 485, 487, 490
4048 14, 15, 16, 17, 20, 23, 26, 28, 31, 33, 39, 42, 44, 45, 46, 58, 59, 62, 67, 68, 69, 72, 73, 77, 79, 82, 83, 84, 86, 87, 88, 92, 93, 95, 96, 97, 99, 103, 106, 108, 112, 114, 115, 117, 118, 121, 123, 124, 125, 127, 128, 130, 132, 134, 135, 137, 138, 139, 140, 141, 143, 144, 145, 147, 149, 150, 152, 155, 156, 157, 158, 159, 162, 164, 166, 167, 168, 171, 175, 176, 177, 178, 179, 184, 186, 190, 192, 195, 196, 199, 201, 203, 205, 206, 207, 208, 210, 214, 215, 216, 217, 218, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 234, 238, 240, 245, 249, 251, 255, 260, 261, 265, 266, 270, 271, 273, 275, 276, 278, 280, 281, 282, 285, 286, 288, 289, 293, 294, 295, 296, 297, 299, 310, 311, 313, 316, 317, 320, 321, 322, 324, 327, 329, 330, 332, 334, 335, 338, 339, 342, 346, 350, 354, 356, 361, 369, 372, 377, 382, 387, 390, 391, 393, 394, 398, 402, 407, 408, 412, 416, 418, 420, 424, 425, 427, 428, 434, 437, 440, 443, 444, 455, 456, 457, 458, 461, 462, 463, 464, 466, 468, 470, 471, 473, 477, 481, 482, 489
4050 18, 30, 35, 81, 89, 94, 98, 101, 116, 154, 165, 172, 181, 185, 189, 198, 209, 230, 237, 246, 250, 253, 254, 267, 269, 272, 274, 284, 305, 306, 308, 325, 331, 348, 352, 355, 362, 364, 378, 380, 383, 386, 388, 397, 403, 410, 414, 415, 422, 430, 433, 439, 442, 459, 467, 469, 474, 480, 483, 484, 486
4270 4
4704 5
8128 6
  1. 1.0 1.1 Yu, Yuyin, Mingsheng Wang, and Yongqiang Li. "A Matrix Approach for Constructing Quadratic APN Functions."