{ "schema_version": "0.2", "name": "[[300,8,14]] two-block code over C5 x D30", "code_type": "CSS", "n": 300, "k": 8, "checks": { "X": [ [ 0, 50, 144, 150, 293 ], [ 1, 38, 78, 151, 296 ], [ 1, 2, 148, 152, 224 ], [ 3, 75, 117, 153, 298 ], [ 4, 64, 76, 154, 212 ], [ 0, 5, 101, 155, 237 ], [ 6, 62, 103, 156, 299 ], [ 7, 63, 104, 157, 225 ], [ 5, 8, 99, 158, 248 ], [ 6, 9, 132, 159, 249 ], [ 7, 10, 88, 153, 160 ], [ 11, 100, 134, 161, 282 ], [ 12, 20, 101, 162, 238 ], [ 13, 91, 102, 163, 239 ], [ 2, 14, 18, 164, 260 ], [ 3, 15, 121, 165, 261 ], [ 4, 16, 122, 156, 166 ], [ 17, 52, 88, 167, 288 ], [ 18, 89, 124, 168, 250 ], [ 19, 90, 125, 169, 251 ], [ 14, 20, 120, 170, 269 ], [ 15, 21, 49, 171, 270 ], [ 11, 16, 22, 159, 172 ], [ 17, 23, 143, 173, 199 ], [ 18, 24, 38, 161, 174 ], [ 19, 25, 112, 162, 175 ], [ 26, 39, 121, 176, 188 ], [ 27, 40, 122, 177, 262 ], [ 28, 115, 123, 178, 263 ], [ 8, 29, 33, 179, 278 ], [ 9, 30, 35, 180, 279 ], [ 10, 31, 36, 165, 181 ], [ 11, 32, 76, 182, 211 ], [ 12, 33, 136, 167, 183 ], [ 13, 34, 137, 168, 184 ], [ 35, 79, 112, 185, 200 ], [ 36, 113, 139, 186, 271 ], [ 37, 114, 140, 187, 272 ], [ 29, 38, 135, 188, 284 ], [ 30, 39, 72, 189, 285 ], [ 23, 31, 40, 171, 190 ], [ 32, 41, 74, 191, 222 ], [ 0, 33, 42, 173, 192 ], [ 26, 34, 43, 174, 193 ], [ 35, 44, 62, 150, 194 ], [ 36, 45, 63, 176, 195 ], [ 37, 46, 130, 177, 196 ], [ 47, 65, 136, 197, 213 ], [ 48, 66, 137, 198, 280 ], [ 49, 133, 138, 199, 281 ], [ 20, 50, 54, 200, 290 ], [ 21, 51, 56, 201, 291 ], [ 22, 52, 57, 180, 202 ], [ 7, 23, 53, 203, 235 ], [ 24, 54, 59, 182, 204 ], [ 25, 55, 60, 183, 205 ], [ 26, 56, 102, 151, 206 ], [ 27, 57, 145, 185, 207 ], [ 28, 58, 146, 186, 208 ], [ 59, 105, 130, 209, 226 ], [ 60, 131, 147, 210, 286 ], [ 51, 61, 132, 211, 287 ], [ 51, 62, 96, 212, 294 ], [ 41, 52, 63, 189, 213 ], [ 53, 64, 98, 214, 246 ], [ 2, 54, 65, 191, 215 ], [ 44, 55, 66, 192, 216 ], [ 3, 56, 67, 152, 217 ], [ 4, 57, 68, 194, 218 ], [ 47, 58, 69, 195, 219 ], [ 59, 70, 89, 154, 220 ], [ 60, 71, 90, 197, 221 ], [ 61, 72, 142, 198, 222 ], [ 73, 92, 145, 223, 240 ], [ 74, 93, 146, 224, 292 ], [ 39, 75, 80, 225, 297 ], [ 40, 76, 81, 201, 226 ], [ 16, 41, 77, 227, 258 ], [ 42, 78, 83, 203, 228 ], [ 43, 79, 84, 204, 229 ], [ 19, 44, 80, 155, 230 ], [ 45, 81, 86, 206, 231 ], [ 46, 82, 87, 207, 232 ], [ 47, 83, 123, 157, 233 ], [ 48, 84, 149, 209, 234 ], [ 49, 75, 85, 210, 235 ], [ 86, 126, 142, 236, 252 ], [ 77, 87, 143, 237, 295 ], [ 77, 88, 119, 238, 267 ], [ 8, 78, 89, 214, 239 ], [ 67, 79, 90, 215, 240 ], [ 9, 80, 91, 158, 241 ], [ 10, 81, 92, 217, 242 ], [ 70, 82, 93, 218, 243 ], [ 12, 83, 94, 160, 244 ], [ 13, 84, 95, 220, 245 ], [ 73, 85, 96, 221, 246 ], [ 86, 97, 113, 163, 247 ], [ 87, 98, 114, 223, 248 ], [ 99, 116, 149, 249, 264 ], [ 31, 64, 100, 250, 276 ], [ 65, 101, 106, 227, 251 ], [ 66, 102, 107, 228, 252 ], [ 34, 67, 103, 164, 253 ], [ 68, 104, 109, 230, 254 ], [ 69, 105, 110, 231, 255 ], [ 37, 70, 106, 166, 256 ], [ 71, 107, 111, 233, 257 ], [ 6, 72, 108, 234, 258 ], [ 73, 109, 138, 169, 259 ], [ 74, 100, 110, 236, 260 ], [ 29, 111, 148, 261, 273 ], [ 21, 103, 112, 170, 262 ], [ 22, 104, 113, 241, 263 ], [ 94, 105, 114, 242, 264 ], [ 24, 106, 115, 172, 265 ], [ 25, 107, 116, 244, 266 ], [ 97, 108, 117, 245, 267 ], [ 27, 109, 118, 175, 268 ], [ 28, 110, 119, 247, 269 ], [ 111, 120, 131, 178, 270 ], [ 55, 91, 121, 179, 271 ], [ 92, 122, 127, 253, 272 ], [ 93, 123, 128, 254, 273 ], [ 58, 94, 124, 181, 274 ], [ 95, 125, 129, 256, 275 ], [ 15, 96, 126, 257, 276 ], [ 61, 97, 127, 184, 277 ], [ 17, 98, 128, 259, 278 ], [ 50, 99, 129, 187, 279 ], [ 42, 124, 130, 190, 280 ], [ 43, 125, 131, 265, 281 ], [ 118, 126, 132, 266, 282 ], [ 45, 127, 133, 193, 283 ], [ 46, 128, 134, 268, 284 ], [ 48, 129, 135, 196, 285 ], [ 82, 115, 136, 202, 286 ], [ 116, 137, 141, 274, 287 ], [ 30, 117, 138, 275, 288 ], [ 85, 118, 139, 205, 289 ], [ 32, 119, 140, 277, 290 ], [ 1, 120, 141, 208, 291 ], [ 68, 139, 142, 216, 292 ], [ 69, 140, 143, 283, 293 ], [ 71, 141, 144, 219, 294 ], [ 108, 133, 145, 229, 295 ], [ 53, 134, 146, 289, 296 ], [ 5, 135, 147, 232, 297 ], [ 95, 147, 148, 243, 298 ], [ 14, 144, 149, 255, 299 ] ], "Z": [ [ 0, 44, 150, 155, 192 ], [ 1, 56, 151, 152, 291 ], [ 2, 67, 152, 164, 215 ], [ 3, 10, 153, 165, 217 ], [ 4, 70, 154, 166, 218 ], [ 5, 80, 155, 158, 297 ], [ 6, 16, 156, 159, 258 ], [ 7, 83, 157, 160, 203 ], [ 8, 91, 158, 179, 239 ], [ 9, 22, 159, 180, 241 ], [ 10, 94, 160, 181, 242 ], [ 11, 24, 161, 172, 182 ], [ 12, 25, 162, 183, 244 ], [ 13, 97, 163, 184, 245 ], [ 14, 103, 164, 170, 299 ], [ 15, 31, 165, 171, 276 ], [ 16, 106, 166, 172, 227 ], [ 17, 33, 167, 173, 278 ], [ 18, 34, 164, 168, 174 ], [ 19, 109, 169, 175, 230 ], [ 20, 112, 162, 170, 200 ], [ 21, 40, 171, 201, 262 ], [ 22, 115, 172, 202, 263 ], [ 23, 42, 173, 190, 203 ], [ 24, 43, 174, 204, 265 ], [ 25, 118, 175, 205, 266 ], [ 26, 45, 176, 193, 206 ], [ 27, 46, 177, 207, 268 ], [ 28, 120, 178, 208, 269 ], [ 29, 121, 179, 188, 261 ], [ 30, 52, 180, 189, 288 ], [ 31, 124, 181, 190, 250 ], [ 32, 54, 182, 191, 290 ], [ 33, 55, 179, 183, 192 ], [ 34, 127, 184, 193, 253 ], [ 35, 57, 180, 185, 194 ], [ 36, 58, 181, 186, 195 ], [ 37, 129, 187, 196, 256 ], [ 26, 38, 151, 174, 188 ], [ 39, 63, 176, 189, 225 ], [ 40, 130, 177, 190, 226 ], [ 41, 65, 191, 213, 227 ], [ 42, 66, 192, 228, 280 ], [ 43, 133, 193, 229, 281 ], [ 44, 68, 194, 216, 230 ], [ 45, 69, 195, 231, 283 ], [ 46, 135, 196, 232, 284 ], [ 47, 71, 197, 219, 233 ], [ 48, 72, 198, 234, 285 ], [ 23, 49, 171, 199, 235 ], [ 35, 50, 150, 200, 279 ], [ 51, 76, 201, 211, 212 ], [ 52, 136, 167, 202, 213 ], [ 53, 78, 203, 214, 296 ], [ 54, 79, 200, 204, 215 ], [ 55, 139, 205, 216, 271 ], [ 56, 81, 201, 206, 217 ], [ 57, 82, 202, 207, 218 ], [ 58, 141, 208, 219, 274 ], [ 59, 84, 204, 209, 220 ], [ 60, 85, 205, 210, 221 ], [ 32, 61, 211, 222, 277 ], [ 4, 62, 156, 194, 212 ], [ 47, 63, 157, 195, 213 ], [ 64, 89, 154, 214, 250 ], [ 65, 90, 197, 215, 251 ], [ 66, 142, 198, 216, 252 ], [ 67, 92, 217, 240, 253 ], [ 68, 93, 218, 254, 292 ], [ 69, 144, 219, 255, 293 ], [ 70, 95, 220, 243, 256 ], [ 71, 96, 221, 257, 294 ], [ 41, 72, 189, 222, 258 ], [ 73, 98, 223, 246, 259 ], [ 2, 74, 191, 224, 260 ], [ 7, 75, 153, 225, 235 ], [ 59, 76, 154, 182, 226 ], [ 77, 101, 227, 237, 238 ], [ 78, 102, 151, 228, 239 ], [ 79, 145, 185, 229, 240 ], [ 80, 104, 225, 230, 241 ], [ 81, 105, 226, 231, 242 ], [ 82, 147, 232, 243, 286 ], [ 83, 107, 228, 233, 244 ], [ 84, 108, 229, 234, 245 ], [ 53, 85, 235, 246, 289 ], [ 86, 110, 231, 236, 247 ], [ 5, 87, 232, 237, 248 ], [ 12, 88, 160, 167, 238 ], [ 13, 89, 168, 220, 239 ], [ 73, 90, 169, 221, 240 ], [ 91, 113, 163, 241, 271 ], [ 92, 114, 223, 242, 272 ], [ 93, 148, 224, 243, 273 ], [ 94, 116, 244, 264, 274 ], [ 95, 117, 245, 275, 298 ], [ 64, 96, 212, 246, 276 ], [ 97, 119, 247, 267, 277 ], [ 8, 98, 214, 248, 278 ], [ 9, 99, 158, 249, 279 ], [ 18, 100, 161, 250, 260 ], [ 19, 101, 155, 162, 251 ], [ 86, 102, 163, 206, 252 ], [ 103, 122, 156, 253, 262 ], [ 104, 123, 157, 254, 263 ], [ 105, 149, 209, 255, 264 ], [ 106, 125, 251, 256, 265 ], [ 107, 126, 252, 257, 266 ], [ 77, 108, 258, 267, 295 ], [ 109, 128, 254, 259, 268 ], [ 14, 110, 255, 260, 269 ], [ 15, 111, 257, 261, 270 ], [ 27, 112, 175, 185, 262 ], [ 28, 113, 186, 247, 263 ], [ 99, 114, 187, 248, 264 ], [ 115, 131, 178, 265, 286 ], [ 116, 132, 249, 266, 287 ], [ 88, 117, 153, 267, 288 ], [ 118, 134, 268, 282, 289 ], [ 20, 119, 238, 269, 290 ], [ 21, 120, 170, 270, 291 ], [ 36, 121, 165, 176, 271 ], [ 37, 122, 166, 177, 272 ], [ 111, 123, 178, 233, 273 ], [ 124, 137, 168, 274, 280 ], [ 125, 138, 169, 275, 281 ], [ 100, 126, 236, 276, 282 ], [ 127, 140, 272, 277, 283 ], [ 29, 128, 273, 278, 284 ], [ 30, 129, 275, 279, 285 ], [ 48, 130, 196, 209, 280 ], [ 49, 131, 210, 270, 281 ], [ 11, 132, 159, 211, 282 ], [ 133, 143, 199, 283, 295 ], [ 38, 134, 161, 284, 296 ], [ 39, 135, 188, 285, 297 ], [ 60, 136, 183, 197, 286 ], [ 61, 137, 184, 198, 287 ], [ 17, 138, 199, 259, 288 ], [ 139, 146, 186, 289, 292 ], [ 50, 140, 187, 290, 293 ], [ 51, 141, 287, 291, 294 ], [ 74, 142, 222, 236, 292 ], [ 0, 143, 173, 237, 293 ], [ 62, 144, 150, 294, 299 ], [ 87, 145, 207, 223, 295 ], [ 1, 146, 208, 224, 296 ], [ 75, 147, 210, 297, 298 ], [ 3, 148, 152, 261, 298 ], [ 6, 149, 234, 249, 299 ] ] }, "distance": { "d": 14, "X": { "value": 14, "confidence": "upper_bound", "witness": [ 8, 11, 91, 94, 113, 116, 132, 146, 161, 181, 186, 214, 250, 296 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 2000, "survived_samples": 2000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1039 ] } }, "Z": { "value": 14, "confidence": "upper_bound", "witness": [ 21, 34, 51, 62, 103, 137, 150, 171, 190, 193, 280, 283, 287, 293 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 2000, "survived_samples": 2000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1040 ] } } }, "provenance": { "authors": [ "Lee, Gideon" ], "construction": "Two-block group-algebra code C(a,b) over C5 x D30 = SmallGroup(150, 11) (order 150), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 300; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 5, 42}, b = {0, 44} as element indices. Check weight 5. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.", "references": [ "arXiv:2610.13880" ], "date": "2026-10-12", "notes": "Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.", "origin": "baseline", "novelty": "known_parameters", "model": "Mimo-V2.6-Flash" }, "family": "2bga-nonabelian" }