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[[310,14,21]] d ≤
n
310
k
14
d
21
kd²/n
19.916
w
8

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Distance

d_X 21 · witness weight 21 (claimed upper_bound)
witness operator (support, 21 qubits)
[34, 45, 87, 100, 103, 104, 105, 142, 146, 168, 169, 172, 175, 192, 201, 220, 244, 252, 277, 303, 309]
d_Z 21 · witness weight 21 (claimed upper_bound)
witness operator (support, 21 qubits)
[3, 17, 51, 77, 89, 101, 104, 106, 124, 130, 136, 150, 229, 232, 239, 256, 268, 277, 284, 287, 301]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @shassinger
provenance submitted through the challenge
novelty novelty not audited
construction Regular 2BGA on C_31 semidirect C_5 with action r=16; supports a=[0, 19, 75, 101], b=[42, 67, 107, 124].
model OpenAI 5.6 Sol (claimed, not verified)
date 2026-07-14
notes Autoresearch sample 413, confirmation seed 8152439. RIS distance upper-bound ladder: 29 (1k trials/side), 22 (2k), 22 (8k), 21 (60k), 21 (1M). Literature novelty unverified.
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 155 · Z-checks 155
H_X (155 checks, sparse supports)
[0, 71, 80, 114, 203, 208, 251, 308] [1, 72, 81, 110, 184, 234, 259, 282] [2, 73, 82, 111, 205, 245, 270, 298] [3, 74, 83, 112, 181, 201, 229, 291] [4, 70, 84, 113, 190, 247, 257, 302] [5, 85, 124, 151, 158, 208, 213, 256] [6, 86, 120, 152, 189, 239, 264, 287] [7, 87, 121, 153, 210, 250, 275, 303] [8, 88, 122, 154, 186, 206, 234, 296] [9, 89, 123, 150, 195, 252, 262, 307] [10, 76, 90, 134, 163, 213, 218, 261] [11, 77, 91, 130, 194, 244, 269, 292] [12, 78, 92, 131, 215, 255, 280, 308] [13, 79, 93, 132, 191, 211, 239, 301] [14, 75, 94, 133, 157, 200, 257, 267] [1, 15, 95, 144, 168, 218, 223, 266] [2, 16, 96, 140, 199, 249, 274, 297] [3, 17, 97, 141, 158, 220, 260, 285] [4, 18, 98, 142, 196, 216, 244, 306] [0, 19, 99, 143, 162, 205, 262, 272] [20, 81, 100, 154, 173, 223, 228, 271] [21, 82, 101, 150, 204, 254, 279, 302] [22, 83, 102, 151, 163, 225, 265, 290] [23, 84, 103, 152, 156, 201, 221, 249] [24, 80, 104, 153, 167, 210, 267, 277] [6, 9, 25, 105, 178, 228, 233, 276] [5, 7, 26, 106, 209, 259, 284, 307] [6, 8, 27, 107, 168, 230, 270, 295] [7, 9, 28, 108, 161, 206, 226, 254] [5, 8, 29, 109, 172, 215, 272, 282] [19, 30, 86, 110, 183, 233, 238, 281] [15, 31, 87, 111, 157, 214, 264, 289] [16, 32, 88, 112, 173, 235, 275, 300] [17, 33, 89, 113, 166, 211, 231, 259] [18, 34, 85, 114, 177, 220, 277, 287] [11, 29, 35, 115, 188, 238, 243, 286] [12, 25, 36, 116, 162, 219, 269, 294] [13, 26, 37, 117, 178, 240, 280, 305] [14, 27, 38, 118, 171, 216, 236, 264] [10, 28, 39, 119, 182, 225, 282, 292] [39, 40, 91, 120, 193, 243, 248, 291] [35, 41, 92, 121, 167, 224, 274, 299] [36, 42, 93, 122, 155, 183, 245, 285] [37, 43, 94, 123, 176, 221, 241, 269] [38, 44, 90, 124, 187, 230, 287, 297] [16, 45, 49, 125, 198, 248, 253, 296] [17, 45, 46, 126, 172, 229, 279, 304] [18, 46, 47, 127, 160, 188, 250, 290] [19, 47, 48, 128, 181, 226, 246, 274] [15, 48, 49, 129, 192, 235, 292, 302] [50, 59, 96, 130, 203, 253, 258, 301] [51, 55, 97, 131, 177, 234, 284, 309] [52, 56, 98, 132, 165, 193, 255, 295] [53, 57, 99, 133, 186, 231, 251, 279] [54, 58, 95, 134, 197, 240, 297, 307] [21, 55, 69, 135, 208, 258, 263, 306] [22, 56, 65, 136, 159, 182, 239, 289] [23, 57, 66, 137, 170, 198, 260, 300] [24, 58, 67, 138, 191, 236, 256, 284] [20, 59, 68, 139, 157, 202, 245, 302] [60, 79, 101, 140, 156, 213, 263, 268] [61, 75, 102, 141, 164, 187, 244, 294] [62, 76, 103, 142, 175, 203, 265, 305] [63, 77, 104, 143, 196, 241, 261, 289] [64, 78, 100, 144, 162, 207, 250, 307] [26, 65, 89, 145, 161, 218, 268, 273] [27, 66, 85, 146, 169, 192, 249, 299] [28, 67, 86, 147, 155, 180, 208, 270] [29, 68, 87, 148, 201, 246, 266, 294] [25, 69, 88, 149, 157, 167, 212, 255] [70, 99, 106, 150, 166, 223, 273, 278] [71, 95, 107, 151, 174, 197, 254, 304] [72, 96, 108, 152, 160, 185, 213, 275] [73, 97, 109, 153, 206, 251, 271, 299] [74, 98, 105, 154, 162, 172, 217, 260] [0, 31, 75, 109, 171, 228, 278, 283] [1, 32, 76, 105, 179, 202, 259, 309] [2, 33, 77, 106, 165, 190, 218, 280] [3, 34, 78, 107, 211, 256, 276, 304] [4, 30, 79, 108, 167, 177, 222, 265] [5, 80, 111, 119, 176, 233, 283, 288] [6, 81, 112, 115, 159, 184, 207, 264] [7, 82, 113, 116, 170, 195, 223, 285] [8, 83, 114, 117, 216, 261, 281, 309] [9, 84, 110, 118, 172, 182, 227, 270] [10, 36, 85, 129, 181, 238, 288, 293] [11, 37, 86, 125, 164, 189, 212, 269] [12, 38, 87, 126, 175, 200, 228, 290] [13, 39, 88, 127, 159, 221, 266, 286] [14, 35, 89, 128, 177, 187, 232, 275] [15, 90, 116, 139, 186, 243, 293, 298] [16, 91, 117, 135, 169, 194, 217, 274] [17, 92, 118, 136, 180, 205, 233, 295] [18, 93, 119, 137, 164, 226, 271, 291] [19, 94, 115, 138, 182, 192, 237, 280] [20, 41, 95, 149, 191, 248, 298, 303] [21, 42, 96, 145, 174, 199, 222, 279] [22, 43, 97, 146, 185, 210, 238, 300] [23, 44, 98, 147, 169, 231, 276, 296] [24, 40, 99, 148, 187, 197, 242, 285] [4, 25, 100, 121, 196, 253, 303, 308] [0, 26, 101, 122, 179, 204, 227, 284] [1, 27, 102, 123, 190, 215, 243, 305] [2, 28, 103, 124, 174, 236, 281, 301] [3, 29, 104, 120, 192, 202, 247, 290] [14, 30, 46, 105, 158, 201, 258, 308] [10, 31, 47, 106, 184, 209, 232, 289] [11, 32, 48, 107, 155, 195, 220, 248] [12, 33, 49, 108, 179, 241, 286, 306] [13, 34, 45, 109, 197, 207, 252, 295] [24, 35, 110, 126, 158, 163, 206, 263] [20, 36, 111, 127, 189, 214, 237, 294] [21, 37, 112, 128, 160, 200, 225, 253] [22, 38, 113, 129, 156, 184, 246, 291] [23, 39, 114, 125, 202, 212, 257, 300] [34, 40, 51, 115, 163, 168, 211, 268] [30, 41, 52, 116, 194, 219, 242, 299] [31, 42, 53, 117, 165, 205, 230, 258] [32, 43, 54, 118, 161, 189, 251, 296] [33, 44, 50, 119, 207, 217, 262, 305] [44, 45, 120, 131, 168, 173, 216, 273] [40, 46, 121, 132, 199, 224, 247, 304] [41, 47, 122, 133, 170, 210, 235, 263] [42, 48, 123, 134, 166, 194, 256, 301] [43, 49, 124, 130, 155, 212, 222, 267] [50, 54, 56, 125, 173, 178, 221, 278] [50, 51, 57, 126, 204, 229, 252, 309] [51, 52, 58, 127, 175, 215, 240, 268] [52, 53, 59, 128, 171, 199, 261, 306] [53, 54, 55, 129, 160, 217, 227, 272] [55, 64, 130, 136, 178, 183, 226, 283] [56, 60, 131, 137, 159, 209, 234, 257] [57, 61, 132, 138, 180, 220, 245, 273] [58, 62, 133, 139, 156, 176, 204, 266] [59, 63, 134, 135, 165, 222, 232, 277] [60, 61, 74, 135, 183, 188, 231, 288] [61, 62, 70, 136, 164, 214, 239, 262] [62, 63, 71, 137, 185, 225, 250, 278] [63, 64, 72, 138, 161, 181, 209, 271] [60, 64, 73, 139, 170, 227, 237, 282] [65, 84, 140, 141, 188, 193, 236, 293] [66, 80, 141, 142, 169, 219, 244, 267] [67, 81, 142, 143, 190, 230, 255, 283] [68, 82, 143, 144, 166, 186, 214, 276] [69, 83, 140, 144, 175, 232, 242, 287] [66, 70, 94, 145, 193, 198, 241, 298] [67, 71, 90, 146, 174, 224, 249, 272] [68, 72, 91, 147, 195, 235, 260, 288] [69, 73, 92, 148, 171, 191, 219, 281] [65, 74, 93, 149, 180, 237, 247, 292] [75, 104, 146, 150, 198, 203, 246, 303] [76, 100, 147, 151, 179, 229, 254, 277] [77, 101, 148, 152, 200, 240, 265, 293] [78, 102, 149, 153, 176, 196, 224, 286] [79, 103, 145, 154, 185, 242, 252, 297]
H_Z (155 checks, sparse supports)
[42, 67, 107, 124, 155, 174, 230, 256] [23, 60, 113, 133, 156, 170, 231, 257] [14, 31, 59, 69, 157, 171, 232, 258] [5, 17, 105, 110, 158, 172, 233, 259] [56, 81, 88, 131, 159, 173, 234, 255] [47, 72, 112, 129, 160, 181, 184, 235] [28, 65, 118, 138, 161, 180, 182, 236] [19, 36, 64, 74, 162, 181, 183, 237] [10, 22, 110, 115, 163, 182, 184, 238] [61, 86, 93, 136, 164, 180, 183, 239] [52, 77, 117, 134, 165, 194, 240, 261] [33, 70, 123, 143, 166, 190, 241, 262] [24, 41, 69, 79, 167, 191, 242, 263] [15, 27, 115, 120, 168, 192, 243, 264] [66, 91, 98, 141, 169, 193, 244, 260] [57, 82, 122, 139, 170, 186, 204, 245] [38, 75, 128, 148, 171, 187, 200, 246] [29, 46, 74, 84, 172, 188, 201, 247] [20, 32, 120, 125, 173, 189, 202, 248] [71, 96, 103, 146, 174, 185, 203, 249] [62, 87, 127, 144, 175, 214, 250, 266] [43, 80, 133, 153, 176, 210, 251, 267] [34, 51, 79, 89, 177, 211, 252, 268] [25, 37, 125, 130, 178, 212, 253, 269] [76, 101, 108, 151, 179, 213, 254, 265] [67, 92, 132, 149, 180, 191, 224, 255] [3, 48, 85, 138, 181, 192, 220, 256] [39, 56, 84, 94, 182, 193, 221, 257] [30, 42, 130, 135, 183, 194, 222, 258] [1, 81, 106, 113, 184, 190, 223, 259] [72, 97, 137, 154, 185, 234, 260, 271] [8, 53, 90, 143, 186, 230, 261, 272] [44, 61, 89, 99, 187, 231, 262, 273] [35, 47, 135, 140, 188, 232, 263, 274] [6, 86, 111, 118, 189, 233, 264, 270] [4, 77, 102, 142, 190, 196, 244, 265] [13, 58, 95, 148, 191, 197, 240, 266] [49, 66, 94, 104, 192, 198, 241, 267] [40, 52, 140, 145, 193, 199, 242, 268] [11, 91, 116, 123, 194, 195, 243, 269] [9, 82, 107, 147, 195, 254, 270, 276] [18, 63, 100, 153, 196, 250, 271, 277] [54, 71, 99, 109, 197, 251, 272, 278] [45, 57, 145, 150, 198, 252, 273, 279] [16, 96, 121, 128, 199, 253, 274, 275] [14, 87, 112, 152, 200, 201, 264, 275] [3, 23, 68, 105, 201, 202, 260, 276] [59, 76, 104, 114, 202, 203, 261, 277] [0, 50, 62, 150, 203, 204, 262, 278] [21, 101, 126, 133, 200, 204, 263, 279] [2, 19, 92, 117, 205, 274, 280, 281] [8, 28, 73, 110, 206, 270, 281, 282] [64, 81, 109, 119, 207, 271, 282, 283] [0, 5, 55, 67, 208, 272, 283, 284] [26, 106, 131, 138, 209, 273, 280, 284] [7, 24, 97, 122, 206, 210, 284, 285] [13, 33, 78, 115, 207, 211, 280, 286] [69, 86, 114, 124, 208, 212, 281, 287] [5, 10, 60, 72, 209, 213, 282, 288] [31, 111, 136, 143, 205, 214, 283, 289] [12, 29, 102, 127, 215, 286, 290, 294] [18, 38, 83, 120, 216, 287, 290, 291] [74, 91, 119, 129, 217, 288, 291, 292] [10, 15, 65, 77, 218, 289, 292, 293] [36, 116, 141, 148, 219, 285, 293, 294] [17, 34, 107, 132, 211, 220, 295, 304] [23, 43, 88, 125, 212, 221, 296, 300] [79, 96, 124, 134, 213, 222, 297, 301] [15, 20, 70, 82, 214, 223, 298, 302] [41, 121, 146, 153, 210, 224, 299, 303] [22, 39, 112, 137, 159, 225, 291, 300] [28, 48, 93, 130, 155, 226, 292, 301] [84, 101, 129, 139, 156, 227, 293, 302] [20, 25, 75, 87, 157, 228, 294, 303] [3, 46, 126, 151, 158, 229, 290, 304] [27, 44, 117, 142, 169, 216, 230, 305] [33, 53, 98, 135, 165, 217, 231, 306] [89, 106, 134, 144, 166, 218, 232, 307] [25, 30, 80, 92, 167, 219, 233, 308] [1, 8, 51, 131, 168, 215, 234, 309] [32, 49, 122, 147, 155, 179, 235, 296] [38, 58, 103, 140, 156, 175, 236, 297] [94, 111, 139, 149, 157, 176, 237, 298] [30, 35, 85, 97, 158, 177, 238, 299] [6, 13, 56, 136, 159, 178, 239, 295] [37, 54, 127, 152, 160, 189, 221, 240] [43, 63, 108, 145, 161, 185, 222, 241] [99, 116, 144, 154, 162, 186, 223, 242] [35, 40, 90, 102, 163, 187, 224, 243] [11, 18, 61, 141, 164, 188, 220, 244] [2, 42, 59, 132, 165, 199, 245, 301] [48, 68, 113, 150, 166, 195, 246, 302] [4, 104, 121, 149, 167, 196, 247, 303] [40, 45, 95, 107, 168, 197, 248, 304] [16, 23, 66, 146, 169, 198, 249, 300] [7, 47, 64, 137, 170, 209, 226, 250] [0, 53, 73, 118, 171, 205, 227, 251] [9, 109, 126, 154, 172, 206, 228, 252] [45, 50, 100, 112, 173, 207, 229, 253] [21, 28, 71, 151, 174, 208, 225, 254] [12, 52, 69, 142, 175, 219, 255, 306] [5, 58, 78, 123, 176, 215, 256, 307] [4, 14, 114, 131, 177, 216, 257, 308] [50, 55, 105, 117, 178, 217, 258, 309] [1, 26, 33, 76, 179, 218, 259, 305] [17, 57, 74, 147, 180, 229, 231, 260] [10, 63, 83, 128, 181, 225, 232, 261] [9, 19, 119, 136, 182, 226, 233, 262] [55, 60, 110, 122, 183, 227, 234, 263] [6, 31, 38, 81, 184, 228, 230, 264] [22, 62, 79, 152, 156, 185, 239, 265] [15, 68, 88, 133, 157, 186, 235, 266] [14, 24, 124, 141, 158, 187, 236, 267] [60, 65, 115, 127, 159, 188, 237, 268] [11, 36, 43, 86, 155, 189, 238, 269] [2, 27, 67, 84, 190, 236, 249, 270] [20, 73, 93, 138, 191, 237, 245, 271] [19, 29, 129, 146, 192, 238, 246, 272] [65, 70, 120, 132, 193, 239, 247, 273] [16, 41, 48, 91, 194, 235, 248, 274] [7, 32, 72, 89, 161, 195, 259, 275] [25, 78, 98, 143, 162, 196, 255, 276] [24, 34, 134, 151, 163, 197, 256, 277] [70, 75, 125, 137, 164, 198, 257, 278] [21, 46, 53, 96, 160, 199, 258, 279] [12, 37, 77, 94, 200, 241, 269, 280] [30, 83, 103, 148, 201, 242, 265, 281] [1, 29, 39, 139, 202, 243, 266, 282] [75, 80, 130, 142, 203, 244, 267, 283] [26, 51, 58, 101, 204, 240, 268, 284] [17, 42, 82, 99, 166, 205, 279, 285] [35, 88, 108, 153, 167, 206, 275, 286] [6, 34, 44, 144, 168, 207, 276, 287] [80, 85, 135, 147, 169, 208, 277, 288] [31, 56, 63, 106, 165, 209, 278, 289] [22, 47, 87, 104, 210, 246, 289, 290] [3, 40, 93, 113, 211, 247, 285, 291] [11, 39, 49, 149, 212, 248, 286, 292] [85, 90, 140, 152, 213, 249, 287, 293] [36, 61, 68, 111, 214, 245, 288, 294] [27, 52, 92, 109, 171, 215, 295, 299] [8, 45, 98, 118, 172, 216, 295, 296] [16, 44, 54, 154, 173, 217, 296, 297] [2, 90, 95, 145, 174, 218, 297, 298] [41, 66, 73, 116, 170, 219, 298, 299] [32, 57, 97, 114, 220, 251, 300, 309] [13, 50, 103, 123, 221, 252, 301, 305] [4, 21, 49, 59, 222, 253, 302, 306] [7, 95, 100, 150, 223, 254, 303, 307] [46, 71, 78, 121, 224, 250, 304, 308] [37, 62, 102, 119, 164, 176, 225, 305] [18, 55, 108, 128, 160, 177, 226, 306] [9, 26, 54, 64, 161, 178, 227, 307] [0, 12, 100, 105, 162, 179, 228, 308] [51, 76, 83, 126, 163, 175, 229, 309]