{ "schema_version": "0.2", "name": "[[252,22,10]] CLP code (arXiv:2610.12782 Table I, weight 7)", "code_type": "CSS", "n": 252, "k": 22, "checks": { "X": [ [ 0, 11, 25, 126, 177, 189, 194 ], [ 1, 28, 58, 127, 183, 189, 190 ], [ 2, 3, 29, 128, 184, 191, 201 ], [ 3, 20, 34, 129, 133, 192, 229 ], [ 4, 8, 17, 130, 186, 193, 207 ], [ 5, 53, 56, 131, 170, 190, 194 ], [ 6, 15, 60, 132, 187, 191, 195 ], [ 6, 7, 37, 133, 139, 196, 215 ], [ 8, 9, 38, 134, 140, 197, 237 ], [ 9, 29, 43, 135, 150, 198, 202 ], [ 10, 23, 51, 136, 188, 193, 199 ], [ 11, 16, 26, 137, 145, 200, 242 ], [ 12, 40, 59, 138, 178, 195, 201 ], [ 13, 59, 61, 129, 139, 202, 222 ], [ 10, 14, 24, 140, 147, 203, 223 ], [ 14, 15, 46, 141, 157, 192, 204 ], [ 16, 17, 47, 142, 158, 205, 210 ], [ 17, 38, 52, 143, 168, 206, 238 ], [ 18, 48, 49, 144, 181, 199, 207 ], [ 1, 19, 32, 145, 153, 208, 227 ], [ 20, 25, 35, 146, 163, 209, 216 ], [ 21, 49, 62, 134, 147, 210, 230 ], [ 12, 22, 62, 143, 148, 196, 211 ], [ 19, 23, 33, 149, 165, 197, 212 ], [ 23, 24, 54, 150, 175, 213, 224 ], [ 25, 26, 55, 151, 176, 214, 245 ], [ 2, 26, 47, 127, 152, 211, 215 ], [ 27, 56, 57, 137, 153, 216, 235 ], [ 7, 28, 41, 154, 171, 200, 217 ], [ 29, 34, 44, 155, 180, 218, 248 ], [ 18, 30, 57, 151, 156, 203, 219 ], [ 18, 21, 31, 157, 161, 220, 231 ], [ 28, 32, 42, 158, 182, 221, 232 ], [ 32, 33, 60, 131, 159, 198, 222 ], [ 4, 34, 35, 132, 160, 219, 223 ], [ 8, 35, 55, 141, 161, 224, 246 ], [ 5, 36, 61, 155, 162, 208, 225 ], [ 15, 37, 50, 163, 185, 226, 236 ], [ 0, 38, 43, 136, 164, 225, 227 ], [ 5, 27, 39, 165, 169, 228, 239 ], [ 27, 30, 40, 126, 166, 204, 229 ], [ 37, 41, 51, 138, 167, 205, 230 ], [ 10, 41, 42, 148, 168, 231, 233 ], [ 11, 43, 44, 149, 169, 232, 250 ], [ 4, 16, 44, 159, 170, 220, 233 ], [ 12, 13, 45, 171, 173, 234, 243 ], [ 24, 46, 58, 144, 172, 209, 235 ], [ 3, 47, 52, 154, 173, 236, 251 ], [ 13, 36, 48, 128, 174, 212, 237 ], [ 36, 39, 49, 135, 175, 238, 240 ], [ 1, 46, 50, 156, 176, 239, 241 ], [ 19, 50, 51, 166, 177, 206, 240 ], [ 0, 20, 52, 167, 178, 228, 241 ], [ 21, 22, 53, 130, 179, 217, 242 ], [ 6, 33, 54, 162, 180, 243, 244 ], [ 2, 9, 55, 172, 181, 234, 244 ], [ 22, 45, 56, 142, 182, 245, 247 ], [ 45, 48, 57, 152, 183, 213, 246 ], [ 7, 54, 58, 174, 184, 214, 247 ], [ 30, 31, 59, 146, 185, 248, 249 ], [ 14, 42, 60, 179, 186, 218, 249 ], [ 31, 53, 61, 160, 187, 221, 250 ], [ 39, 40, 62, 164, 188, 226, 251 ], [ 63, 74, 88, 126, 148, 190, 229 ], [ 64, 91, 121, 127, 135, 194, 215 ], [ 65, 66, 92, 128, 156, 195, 237 ], [ 66, 83, 97, 129, 183, 202, 204 ], [ 67, 71, 80, 130, 162, 199, 242 ], [ 68, 116, 119, 131, 141, 189, 222 ], [ 69, 78, 123, 132, 142, 201, 223 ], [ 69, 70, 100, 133, 170, 192, 211 ], [ 71, 72, 101, 134, 187, 210, 212 ], [ 72, 92, 106, 135, 157, 222, 238 ], [ 73, 86, 114, 136, 146, 207, 227 ], [ 74, 79, 89, 137, 188, 216, 217 ], [ 75, 103, 122, 138, 149, 191, 230 ], [ 76, 122, 124, 139, 177, 196, 198 ], [ 73, 77, 87, 140, 178, 197, 219 ], [ 77, 78, 109, 141, 143, 224, 229 ], [ 79, 80, 110, 142, 165, 230, 245 ], [ 80, 101, 115, 131, 143, 211, 240 ], [ 81, 111, 112, 144, 154, 193, 235 ], [ 64, 82, 95, 145, 181, 200, 225 ], [ 83, 88, 98, 146, 171, 235, 248 ], [ 84, 112, 125, 147, 184, 203, 205 ], [ 75, 85, 125, 148, 150, 215, 231 ], [ 82, 86, 96, 149, 151, 232, 237 ], [ 86, 87, 117, 126, 150, 198, 246 ], [ 88, 89, 118, 138, 151, 219, 247 ], [ 65, 89, 110, 152, 166, 196, 246 ], [ 90, 119, 120, 153, 186, 208, 209 ], [ 70, 91, 104, 154, 155, 236, 242 ], [ 92, 97, 107, 144, 155, 225, 249 ], [ 81, 93, 120, 156, 158, 223, 239 ], [ 81, 84, 94, 127, 157, 204, 233 ], [ 91, 95, 105, 128, 158, 205, 250 ], [ 95, 96, 123, 152, 159, 202, 233 ], [ 67, 97, 98, 160, 174, 203, 250 ], [ 71, 98, 118, 139, 161, 213, 220 ], [ 68, 99, 124, 162, 163, 227, 243 ], [ 78, 100, 113, 130, 163, 209, 251 ], [ 63, 101, 106, 164, 179, 208, 251 ], [ 68, 90, 102, 132, 165, 212, 241 ], [ 90, 93, 103, 159, 166, 192, 240 ], [ 100, 104, 114, 160, 167, 210, 241 ], [ 73, 104, 105, 129, 168, 206, 220 ], [ 74, 106, 107, 147, 169, 221, 228 ], [ 67, 79, 107, 170, 175, 194, 231 ], [ 75, 76, 108, 136, 171, 217, 244 ], [ 87, 109, 121, 164, 172, 216, 244 ], [ 66, 110, 115, 153, 173, 226, 234 ], [ 76, 99, 111, 167, 174, 197, 247 ], [ 99, 102, 112, 133, 175, 206, 213 ], [ 64, 109, 113, 134, 176, 214, 228 ], [ 82, 113, 114, 161, 177, 189, 238 ], [ 63, 83, 115, 178, 182, 201, 239 ], [ 84, 85, 116, 172, 179, 200, 249 ], [ 69, 96, 117, 137, 180, 218, 234 ], [ 65, 72, 118, 181, 185, 207, 243 ], [ 85, 108, 119, 140, 182, 214, 221 ], [ 108, 111, 120, 168, 183, 190, 224 ], [ 70, 117, 121, 169, 184, 191, 245 ], [ 93, 94, 122, 145, 185, 218, 226 ], [ 77, 105, 123, 173, 186, 193, 248 ], [ 94, 116, 124, 176, 187, 195, 232 ], [ 102, 103, 125, 180, 188, 199, 236 ] ], "Z": [ [ 0, 40, 63, 87, 126, 164, 178 ], [ 1, 26, 64, 94, 127, 145, 176 ], [ 2, 48, 65, 95, 128, 152, 181 ], [ 3, 13, 66, 105, 128, 129, 173 ], [ 4, 53, 67, 100, 130, 160, 170 ], [ 5, 33, 68, 80, 131, 162, 165 ], [ 6, 34, 69, 102, 132, 133, 180 ], [ 3, 7, 70, 112, 133, 154, 184 ], [ 8, 21, 71, 113, 130, 134, 161 ], [ 9, 49, 64, 72, 134, 135, 181 ], [ 10, 38, 73, 108, 136, 140, 168 ], [ 11, 27, 74, 117, 126, 137, 169 ], [ 12, 41, 75, 88, 138, 148, 171 ], [ 7, 13, 76, 98, 139, 171, 174 ], [ 8, 14, 77, 119, 140, 141, 186 ], [ 15, 35, 68, 78, 132, 141, 163 ], [ 16, 56, 69, 79, 137, 142, 170 ], [ 17, 22, 78, 80, 130, 142, 143 ], [ 18, 46, 81, 92, 144, 156, 157 ], [ 11, 19, 82, 122, 145, 149, 177 ], [ 20, 59, 73, 83, 129, 146, 178 ], [ 14, 21, 84, 106, 147, 157, 179 ], [ 22, 42, 63, 85, 148, 179, 182 ], [ 23, 43, 75, 86, 136, 149, 150 ], [ 9, 24, 85, 87, 140, 150, 172 ], [ 25, 30, 86, 88, 126, 146, 151 ], [ 26, 57, 89, 96, 137, 151, 152 ], [ 19, 27, 90, 110, 153, 165, 166 ], [ 28, 47, 81, 91, 127, 154, 158 ], [ 29, 36, 91, 92, 128, 135, 155 ], [ 30, 50, 65, 93, 156, 166, 185 ], [ 15, 31, 72, 94, 157, 185, 187 ], [ 16, 32, 93, 95, 145, 158, 159 ], [ 33, 44, 96, 103, 149, 159, 180 ], [ 34, 61, 97, 104, 129, 155, 160 ], [ 31, 35, 98, 114, 146, 160, 161 ], [ 36, 54, 67, 99, 162, 174, 175 ], [ 20, 37, 99, 100, 133, 163, 167 ], [ 38, 62, 101, 109, 134, 143, 164 ], [ 23, 39, 79, 102, 165, 175, 188 ], [ 40, 51, 89, 103, 138, 166, 188 ], [ 41, 52, 104, 111, 154, 167, 168 ], [ 17, 42, 105, 120, 158, 168, 186 ], [ 39, 43, 106, 121, 135, 164, 169 ], [ 5, 44, 70, 107, 155, 169, 170 ], [ 28, 45, 83, 108, 171, 182, 183 ], [ 46, 55, 109, 116, 141, 172, 176 ], [ 45, 47, 110, 123, 142, 152, 173 ], [ 48, 58, 97, 111, 144, 174, 183 ], [ 24, 49, 107, 112, 144, 147, 175 ], [ 25, 50, 113, 124, 163, 176, 177 ], [ 0, 51, 76, 114, 136, 167, 177 ], [ 12, 52, 77, 115, 143, 173, 178 ], [ 53, 60, 101, 116, 131, 179, 187 ], [ 29, 54, 117, 125, 150, 180, 184 ], [ 18, 55, 82, 118, 151, 161, 181 ], [ 32, 56, 115, 119, 131, 153, 182 ], [ 1, 57, 66, 120, 153, 156, 183 ], [ 2, 58, 84, 121, 127, 172, 184 ], [ 37, 59, 118, 122, 138, 139, 185 ], [ 4, 60, 90, 123, 132, 159, 186 ], [ 6, 61, 71, 124, 139, 162, 187 ], [ 10, 62, 74, 125, 147, 148, 188 ], [ 0, 1, 68, 114, 189, 227, 241 ], [ 1, 5, 63, 120, 190, 208, 239 ], [ 2, 6, 75, 121, 191, 215, 244 ], [ 3, 15, 70, 103, 191, 192, 236 ], [ 4, 10, 81, 123, 193, 223, 233 ], [ 0, 5, 64, 107, 194, 225, 228 ], [ 6, 12, 65, 124, 195, 196, 243 ], [ 7, 22, 76, 89, 196, 217, 247 ], [ 8, 23, 77, 111, 193, 197, 224 ], [ 9, 33, 76, 87, 197, 198, 244 ], [ 10, 18, 67, 125, 199, 203, 231 ], [ 11, 28, 82, 116, 189, 200, 232 ], [ 2, 12, 69, 115, 201, 211, 234 ], [ 9, 13, 66, 96, 202, 234, 237 ], [ 14, 30, 84, 97, 203, 204, 249 ], [ 15, 40, 66, 94, 195, 204, 226 ], [ 16, 41, 84, 95, 200, 205, 233 ], [ 17, 51, 105, 112, 193, 205, 206 ], [ 4, 18, 73, 118, 207, 219, 220 ], [ 19, 36, 90, 101, 208, 212, 240 ], [ 20, 46, 90, 100, 192, 209, 241 ], [ 16, 21, 71, 104, 210, 220, 242 ], [ 22, 26, 70, 80, 211, 242, 245 ], [ 23, 48, 71, 102, 199, 212, 213 ], [ 24, 57, 98, 112, 203, 213, 235 ], [ 25, 58, 113, 119, 189, 209, 214 ], [ 7, 26, 64, 85, 200, 214, 215 ], [ 20, 27, 74, 109, 216, 228, 229 ], [ 28, 53, 74, 108, 190, 217, 221 ], [ 29, 60, 117, 122, 191, 198, 218 ], [ 30, 34, 77, 88, 219, 229, 248 ], [ 31, 44, 98, 105, 220, 248, 250 ], [ 32, 61, 106, 119, 208, 221, 222 ], [ 13, 33, 68, 72, 212, 222, 243 ], [ 14, 34, 69, 93, 192, 218, 223 ], [ 24, 35, 78, 120, 209, 223, 224 ], [ 36, 38, 82, 92, 225, 237, 238 ], [ 37, 62, 110, 122, 196, 226, 230 ], [ 19, 38, 73, 99, 197, 206, 227 ], [ 39, 52, 106, 113, 228, 238, 251 ], [ 3, 40, 63, 78, 201, 229, 251 ], [ 21, 41, 75, 79, 217, 230, 231 ], [ 31, 42, 85, 107, 221, 231, 249 ], [ 32, 43, 86, 124, 198, 227, 232 ], [ 42, 44, 94, 96, 218, 232, 233 ], [ 45, 55, 110, 117, 234, 245, 246 ], [ 27, 46, 81, 83, 204, 235, 239 ], [ 37, 47, 91, 125, 205, 215, 236 ], [ 8, 48, 65, 86, 207, 237, 246 ], [ 17, 49, 72, 114, 207, 210, 238 ], [ 39, 50, 93, 115, 226, 239, 240 ], [ 49, 51, 80, 103, 199, 230, 240 ], [ 50, 52, 102, 104, 206, 236, 241 ], [ 11, 53, 67, 91, 194, 242, 250 ], [ 45, 54, 99, 118, 213, 243, 247 ], [ 54, 55, 108, 109, 214, 224, 244 ], [ 25, 56, 79, 121, 194, 216, 245 ], [ 35, 57, 87, 89, 216, 219, 246 ], [ 56, 58, 88, 111, 190, 235, 247 ], [ 29, 59, 83, 123, 201, 202, 248 ], [ 59, 60, 92, 116, 195, 222, 249 ], [ 43, 61, 95, 97, 202, 225, 250 ], [ 47, 62, 100, 101, 210, 211, 251 ] ] }, "distance": { "d": 10, "X": { "value": 10, "confidence": "upper_bound", "witness": [ 194, 202, 211, 228, 229, 234, 245, 248, 250, 251 ], "witness_provenance": { "found_by": [ "@MathysRennela" ], "date": "2026-10-12", "found_at_samples": 4000, "survived_samples": 4000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 11 ] } }, "Z": { "value": 10, "confidence": "upper_bound", "witness": [ 65, 66, 74, 79, 88, 97, 98, 107, 110, 118 ], "witness_provenance": { "found_by": [ "@MathysRennela" ], "date": "2026-10-12", "found_at_samples": 4000, "survived_samples": 4000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 12 ] } } }, "provenance": { "authors": [ "Rajpurohit, Rajendra Prasad", "Lalitha, V.", "Garani, Shayan Srinivasa", "@MathysRennela" ], "construction": "Coset lifted product (CLP) code of arXiv:2610.12782, Definition III.1, 1x1 over 2x2 layout: a protograph A over F_2[G] acting by the LEFT coset action of G on the cosets G/H, and a protograph B over F_2[N_G(H)] acting by the RIGHT coset action of the normaliser on the same cosets. G = SmallGroup(126,8), H = (non-normal, core free), m = [G:H], n = 4m = 252. Elements are named by the polycyclic generating sequence f_1,...,f_r of SmallGroup(126,8), as in the paper's Appendix A. CSS commutation is automatic (L(g) and R(n) commute for every g in G and n in N_G(H), so each block of H_X H_Z^T is L R + R L = 0 over F_2); no search for it is needed. n, k and the check weight 7 reproduce the paper's Table I exactly. Literature baseline seeded from the published parameters: this entry is a REPRODUCTION built from the paper's printed data, not a new construction and not a new parameter set. The paper certifies d = 10 by integer program; this entry carries witness-backed upper bounds from our own randomized GF(2) search, which is a weaker claim.", "references": [ "arXiv:2610.12782", "arXiv:2606.17268" ], "date": "2026-10-12", "notes": "Literature baseline: a reproduction of the published parameters in arXiv:2610.12782 (Table I), not a new construction and not a new parameter set. The group, subgroup and protographs are the paper's Appendix A data, rebuilt from GAP SmallGroup(l,i); n, k and the check weight reproduce the paper exactly. Reproduced by Space Bunny Alpha 1.0. The distance here is a witness-backed upper bound from our own randomized GF(2) search, a weaker claim than the paper's integer-program certification. See the accompanying note for the full reproduction recipe.", "origin": "baseline", "novelty": "known_parameters", "model": "Space Bunny Alpha 1.0" }, "family": "2bga-coset" }