{ "schema_version": "0.2", "name": "[[384,16,23]] weight-7 two-block group-algebra code on C24:C8(r=17)", "code_type": "CSS", "n": 384, "k": 16, "checks": { "X": [ [ 0, 155, 166, 192, 211, 276, 369 ], [ 1, 156, 167, 193, 213, 276, 306 ], [ 2, 157, 160, 194, 213, 278, 371 ], [ 3, 158, 161, 195, 215, 278, 308 ], [ 4, 159, 162, 196, 215, 272, 373 ], [ 5, 152, 163, 197, 209, 272, 310 ], [ 6, 153, 164, 198, 209, 274, 375 ], [ 7, 154, 165, 199, 211, 274, 304 ], [ 8, 99, 174, 200, 219, 284, 377 ], [ 9, 100, 175, 201, 221, 284, 314 ], [ 10, 101, 168, 202, 221, 286, 379 ], [ 11, 102, 169, 203, 223, 286, 316 ], [ 12, 103, 170, 204, 223, 280, 381 ], [ 13, 96, 171, 205, 217, 280, 318 ], [ 14, 97, 172, 206, 217, 282, 383 ], [ 15, 98, 173, 207, 219, 282, 312 ], [ 16, 43, 182, 193, 208, 227, 292 ], [ 17, 44, 183, 209, 229, 292, 322 ], [ 18, 45, 176, 195, 210, 229, 294 ], [ 19, 46, 177, 211, 231, 294, 324 ], [ 20, 47, 178, 197, 212, 231, 288 ], [ 21, 40, 179, 213, 225, 288, 326 ], [ 22, 41, 180, 199, 214, 225, 290 ], [ 23, 42, 181, 215, 227, 290, 320 ], [ 24, 179, 190, 201, 216, 235, 300 ], [ 25, 180, 191, 217, 237, 300, 330 ], [ 26, 181, 184, 203, 218, 237, 302 ], [ 27, 182, 185, 219, 239, 302, 332 ], [ 28, 183, 186, 205, 220, 239, 296 ], [ 29, 176, 187, 221, 233, 296, 334 ], [ 30, 177, 188, 207, 222, 233, 298 ], [ 31, 178, 189, 223, 235, 298, 328 ], [ 6, 32, 123, 209, 224, 243, 308 ], [ 7, 33, 124, 225, 245, 308, 338 ], [ 0, 34, 125, 211, 226, 245, 310 ], [ 1, 35, 126, 227, 247, 310, 340 ], [ 2, 36, 127, 213, 228, 247, 304 ], [ 3, 37, 120, 229, 241, 304, 342 ], [ 4, 38, 121, 215, 230, 241, 306 ], [ 5, 39, 122, 231, 243, 306, 336 ], [ 14, 40, 67, 217, 232, 251, 316 ], [ 15, 41, 68, 233, 253, 316, 346 ], [ 8, 42, 69, 219, 234, 253, 318 ], [ 9, 43, 70, 235, 255, 318, 348 ], [ 10, 44, 71, 221, 236, 255, 312 ], [ 11, 45, 64, 237, 249, 312, 350 ], [ 12, 46, 65, 223, 238, 249, 314 ], [ 13, 47, 66, 239, 251, 314, 344 ], [ 11, 22, 48, 225, 240, 259, 324 ], [ 12, 23, 49, 241, 261, 324, 354 ], [ 13, 16, 50, 227, 242, 261, 326 ], [ 14, 17, 51, 243, 263, 326, 356 ], [ 15, 18, 52, 229, 244, 263, 320 ], [ 8, 19, 53, 245, 257, 320, 358 ], [ 9, 20, 54, 231, 246, 257, 322 ], [ 10, 21, 55, 247, 259, 322, 352 ], [ 30, 56, 147, 233, 248, 267, 332 ], [ 31, 57, 148, 249, 269, 332, 362 ], [ 24, 58, 149, 235, 250, 269, 334 ], [ 25, 59, 150, 251, 271, 334, 364 ], [ 26, 60, 151, 237, 252, 271, 328 ], [ 27, 61, 144, 253, 265, 328, 366 ], [ 28, 62, 145, 239, 254, 265, 330 ], [ 29, 63, 146, 255, 267, 330, 360 ], [ 38, 64, 91, 241, 256, 275, 340 ], [ 39, 65, 92, 257, 277, 340, 370 ], [ 32, 66, 93, 243, 258, 277, 342 ], [ 33, 67, 94, 259, 279, 342, 372 ], [ 34, 68, 95, 245, 260, 279, 336 ], [ 35, 69, 88, 261, 273, 336, 374 ], [ 36, 70, 89, 247, 262, 273, 338 ], [ 37, 71, 90, 263, 275, 338, 368 ], [ 35, 46, 72, 249, 264, 283, 348 ], [ 36, 47, 73, 265, 285, 348, 378 ], [ 37, 40, 74, 251, 266, 285, 350 ], [ 38, 41, 75, 267, 287, 350, 380 ], [ 39, 42, 76, 253, 268, 287, 344 ], [ 32, 43, 77, 269, 281, 344, 382 ], [ 33, 44, 78, 255, 270, 281, 346 ], [ 34, 45, 79, 271, 283, 346, 376 ], [ 54, 80, 171, 257, 272, 291, 356 ], [ 55, 81, 172, 194, 273, 293, 356 ], [ 48, 82, 173, 259, 274, 293, 358 ], [ 49, 83, 174, 196, 275, 295, 358 ], [ 50, 84, 175, 261, 276, 295, 352 ], [ 51, 85, 168, 198, 277, 289, 352 ], [ 52, 86, 169, 263, 278, 289, 354 ], [ 53, 87, 170, 192, 279, 291, 354 ], [ 62, 88, 115, 265, 280, 299, 364 ], [ 63, 89, 116, 202, 281, 301, 364 ], [ 56, 90, 117, 267, 282, 301, 366 ], [ 57, 91, 118, 204, 283, 303, 366 ], [ 58, 92, 119, 269, 284, 303, 360 ], [ 59, 93, 112, 206, 285, 297, 360 ], [ 60, 94, 113, 271, 286, 297, 362 ], [ 61, 95, 114, 200, 287, 299, 362 ], [ 59, 70, 96, 273, 288, 307, 372 ], [ 60, 71, 97, 210, 289, 309, 372 ], [ 61, 64, 98, 275, 290, 309, 374 ], [ 62, 65, 99, 212, 291, 311, 374 ], [ 63, 66, 100, 277, 292, 311, 368 ], [ 56, 67, 101, 214, 293, 305, 368 ], [ 57, 68, 102, 279, 294, 305, 370 ], [ 58, 69, 103, 208, 295, 307, 370 ], [ 3, 78, 104, 281, 296, 315, 380 ], [ 4, 79, 105, 218, 297, 317, 380 ], [ 5, 72, 106, 283, 298, 317, 382 ], [ 6, 73, 107, 220, 299, 319, 382 ], [ 7, 74, 108, 285, 300, 319, 376 ], [ 0, 75, 109, 222, 301, 313, 376 ], [ 1, 76, 110, 287, 302, 313, 378 ], [ 2, 77, 111, 216, 303, 315, 378 ], [ 86, 112, 139, 196, 289, 304, 323 ], [ 87, 113, 140, 196, 226, 305, 325 ], [ 80, 114, 141, 198, 291, 306, 325 ], [ 81, 115, 142, 198, 228, 307, 327 ], [ 82, 116, 143, 192, 293, 308, 327 ], [ 83, 117, 136, 192, 230, 309, 321 ], [ 84, 118, 137, 194, 295, 310, 321 ], [ 85, 119, 138, 194, 224, 311, 323 ], [ 83, 94, 120, 204, 297, 312, 331 ], [ 84, 95, 121, 204, 234, 313, 333 ], [ 85, 88, 122, 206, 299, 314, 333 ], [ 86, 89, 123, 206, 236, 315, 335 ], [ 87, 90, 124, 200, 301, 316, 335 ], [ 80, 91, 125, 200, 238, 317, 329 ], [ 81, 92, 126, 202, 303, 318, 329 ], [ 82, 93, 127, 202, 232, 319, 331 ], [ 27, 102, 128, 212, 305, 320, 339 ], [ 28, 103, 129, 212, 242, 321, 341 ], [ 29, 96, 130, 214, 307, 322, 341 ], [ 30, 97, 131, 214, 244, 323, 343 ], [ 31, 98, 132, 208, 309, 324, 343 ], [ 24, 99, 133, 208, 246, 325, 337 ], [ 25, 100, 134, 210, 311, 326, 337 ], [ 26, 101, 135, 210, 240, 327, 339 ], [ 110, 136, 163, 220, 313, 328, 347 ], [ 111, 137, 164, 220, 250, 329, 349 ], [ 104, 138, 165, 222, 315, 330, 349 ], [ 105, 139, 166, 222, 252, 331, 351 ], [ 106, 140, 167, 216, 317, 332, 351 ], [ 107, 141, 160, 216, 254, 333, 345 ], [ 108, 142, 161, 218, 319, 334, 345 ], [ 109, 143, 162, 218, 248, 335, 347 ], [ 107, 118, 144, 228, 321, 336, 355 ], [ 108, 119, 145, 228, 258, 337, 357 ], [ 109, 112, 146, 230, 323, 338, 357 ], [ 110, 113, 147, 230, 260, 339, 359 ], [ 111, 114, 148, 224, 325, 340, 359 ], [ 104, 115, 149, 224, 262, 341, 353 ], [ 105, 116, 150, 226, 327, 342, 353 ], [ 106, 117, 151, 226, 256, 343, 355 ], [ 51, 126, 152, 236, 329, 344, 363 ], [ 52, 127, 153, 236, 266, 345, 365 ], [ 53, 120, 154, 238, 331, 346, 365 ], [ 54, 121, 155, 238, 268, 347, 367 ], [ 55, 122, 156, 232, 333, 348, 367 ], [ 48, 123, 157, 232, 270, 349, 361 ], [ 49, 124, 158, 234, 335, 350, 361 ], [ 50, 125, 159, 234, 264, 351, 363 ], [ 134, 160, 187, 244, 337, 352, 371 ], [ 135, 161, 188, 244, 274, 353, 373 ], [ 128, 162, 189, 246, 339, 354, 373 ], [ 129, 163, 190, 246, 276, 355, 375 ], [ 130, 164, 191, 240, 341, 356, 375 ], [ 131, 165, 184, 240, 278, 357, 369 ], [ 132, 166, 185, 242, 343, 358, 369 ], [ 133, 167, 186, 242, 272, 359, 371 ], [ 131, 142, 168, 252, 345, 360, 379 ], [ 132, 143, 169, 252, 282, 361, 381 ], [ 133, 136, 170, 254, 347, 362, 381 ], [ 134, 137, 171, 254, 284, 363, 383 ], [ 135, 138, 172, 248, 349, 364, 383 ], [ 128, 139, 173, 248, 286, 365, 377 ], [ 129, 140, 174, 250, 351, 366, 377 ], [ 130, 141, 175, 250, 280, 367, 379 ], [ 75, 150, 176, 195, 260, 353, 368 ], [ 76, 151, 177, 197, 260, 290, 369 ], [ 77, 144, 178, 197, 262, 355, 370 ], [ 78, 145, 179, 199, 262, 292, 371 ], [ 79, 146, 180, 199, 256, 357, 372 ], [ 72, 147, 181, 193, 256, 294, 373 ], [ 73, 148, 182, 193, 258, 359, 374 ], [ 74, 149, 183, 195, 258, 288, 375 ], [ 19, 158, 184, 203, 268, 361, 376 ], [ 20, 159, 185, 205, 268, 298, 377 ], [ 21, 152, 186, 205, 270, 363, 378 ], [ 22, 153, 187, 207, 270, 300, 379 ], [ 23, 154, 188, 207, 264, 365, 380 ], [ 16, 155, 189, 201, 264, 302, 381 ], [ 17, 156, 190, 201, 266, 367, 382 ], [ 18, 157, 191, 203, 266, 296, 383 ] ], "Z": [ [ 0, 87, 116, 117, 192, 226, 301 ], [ 1, 16, 181, 182, 193, 227, 302 ], [ 2, 81, 118, 119, 194, 228, 303 ], [ 3, 18, 176, 183, 195, 229, 296 ], [ 4, 83, 112, 113, 196, 230, 297 ], [ 5, 20, 177, 178, 197, 231, 298 ], [ 6, 85, 114, 115, 198, 224, 299 ], [ 7, 22, 179, 180, 199, 225, 300 ], [ 8, 95, 124, 125, 200, 234, 245 ], [ 9, 24, 189, 190, 201, 235, 246 ], [ 10, 89, 126, 127, 202, 236, 247 ], [ 11, 26, 184, 191, 203, 237, 240 ], [ 12, 91, 120, 121, 204, 238, 241 ], [ 13, 28, 185, 186, 205, 239, 242 ], [ 14, 93, 122, 123, 206, 232, 243 ], [ 15, 30, 187, 188, 207, 233, 244 ], [ 16, 103, 132, 133, 208, 242, 381 ], [ 5, 6, 17, 32, 209, 243, 382 ], [ 18, 97, 134, 135, 210, 244, 383 ], [ 0, 7, 19, 34, 211, 245, 376 ], [ 20, 99, 128, 129, 212, 246, 377 ], [ 1, 2, 21, 36, 213, 247, 378 ], [ 22, 101, 130, 131, 214, 240, 379 ], [ 3, 4, 23, 38, 215, 241, 380 ], [ 24, 111, 140, 141, 216, 250, 325 ], [ 13, 14, 25, 40, 217, 251, 326 ], [ 26, 105, 142, 143, 218, 252, 327 ], [ 8, 15, 27, 42, 219, 253, 320 ], [ 28, 107, 136, 137, 220, 254, 321 ], [ 9, 10, 29, 44, 221, 255, 322 ], [ 30, 109, 138, 139, 222, 248, 323 ], [ 11, 12, 31, 46, 223, 249, 324 ], [ 32, 119, 148, 149, 224, 258, 269 ], [ 21, 22, 33, 48, 225, 259, 270 ], [ 34, 113, 150, 151, 226, 260, 271 ], [ 16, 23, 35, 50, 227, 261, 264 ], [ 36, 115, 144, 145, 228, 262, 265 ], [ 17, 18, 37, 52, 229, 263, 266 ], [ 38, 117, 146, 147, 230, 256, 267 ], [ 19, 20, 39, 54, 231, 257, 268 ], [ 40, 127, 156, 157, 213, 232, 266 ], [ 29, 30, 41, 56, 214, 233, 267 ], [ 42, 121, 158, 159, 215, 234, 268 ], [ 24, 31, 43, 58, 208, 235, 269 ], [ 44, 123, 152, 153, 209, 236, 270 ], [ 25, 26, 45, 60, 210, 237, 271 ], [ 46, 125, 154, 155, 211, 238, 264 ], [ 27, 28, 47, 62, 212, 239, 265 ], [ 48, 135, 164, 165, 240, 274, 349 ], [ 37, 38, 49, 64, 241, 275, 350 ], [ 50, 129, 166, 167, 242, 276, 351 ], [ 32, 39, 51, 66, 243, 277, 344 ], [ 52, 131, 160, 161, 244, 278, 345 ], [ 33, 34, 53, 68, 245, 279, 346 ], [ 54, 133, 162, 163, 246, 272, 347 ], [ 35, 36, 55, 70, 247, 273, 348 ], [ 56, 143, 172, 173, 248, 282, 293 ], [ 45, 46, 57, 72, 249, 283, 294 ], [ 58, 137, 174, 175, 250, 284, 295 ], [ 40, 47, 59, 74, 251, 285, 288 ], [ 60, 139, 168, 169, 252, 286, 289 ], [ 41, 42, 61, 76, 253, 287, 290 ], [ 62, 141, 170, 171, 254, 280, 291 ], [ 43, 44, 63, 78, 255, 281, 292 ], [ 64, 151, 180, 181, 237, 256, 290 ], [ 53, 54, 65, 80, 238, 257, 291 ], [ 66, 145, 182, 183, 239, 258, 292 ], [ 48, 55, 67, 82, 232, 259, 293 ], [ 68, 147, 176, 177, 233, 260, 294 ], [ 49, 50, 69, 84, 234, 261, 295 ], [ 70, 149, 178, 179, 235, 262, 288 ], [ 51, 52, 71, 86, 236, 263, 289 ], [ 72, 159, 188, 189, 264, 298, 373 ], [ 61, 62, 73, 88, 265, 299, 374 ], [ 74, 153, 190, 191, 266, 300, 375 ], [ 56, 63, 75, 90, 267, 301, 368 ], [ 76, 155, 184, 185, 268, 302, 369 ], [ 57, 58, 77, 92, 269, 303, 370 ], [ 78, 157, 186, 187, 270, 296, 371 ], [ 59, 60, 79, 94, 271, 297, 372 ], [ 4, 5, 80, 167, 272, 306, 317 ], [ 69, 70, 81, 96, 273, 307, 318 ], [ 6, 7, 82, 161, 274, 308, 319 ], [ 64, 71, 83, 98, 275, 309, 312 ], [ 0, 1, 84, 163, 276, 310, 313 ], [ 65, 66, 85, 100, 277, 311, 314 ], [ 2, 3, 86, 165, 278, 304, 315 ], [ 67, 68, 87, 102, 279, 305, 316 ], [ 12, 13, 88, 175, 261, 280, 314 ], [ 77, 78, 89, 104, 262, 281, 315 ], [ 14, 15, 90, 169, 263, 282, 316 ], [ 72, 79, 91, 106, 256, 283, 317 ], [ 8, 9, 92, 171, 257, 284, 318 ], [ 73, 74, 93, 108, 258, 285, 319 ], [ 10, 11, 94, 173, 259, 286, 312 ], [ 75, 76, 95, 110, 260, 287, 313 ], [ 20, 21, 96, 183, 205, 288, 322 ], [ 85, 86, 97, 112, 206, 289, 323 ], [ 22, 23, 98, 177, 207, 290, 324 ], [ 80, 87, 99, 114, 200, 291, 325 ], [ 16, 17, 100, 179, 201, 292, 326 ], [ 81, 82, 101, 116, 202, 293, 327 ], [ 18, 19, 102, 181, 203, 294, 320 ], [ 83, 84, 103, 118, 204, 295, 321 ], [ 28, 29, 104, 191, 296, 330, 341 ], [ 93, 94, 105, 120, 297, 331, 342 ], [ 30, 31, 106, 185, 298, 332, 343 ], [ 88, 95, 107, 122, 299, 333, 336 ], [ 24, 25, 108, 187, 300, 334, 337 ], [ 89, 90, 109, 124, 301, 335, 338 ], [ 26, 27, 110, 189, 302, 328, 339 ], [ 91, 92, 111, 126, 303, 329, 340 ], [ 7, 36, 37, 112, 285, 304, 338 ], [ 101, 102, 113, 128, 286, 305, 339 ], [ 1, 38, 39, 114, 287, 306, 340 ], [ 96, 103, 115, 130, 280, 307, 341 ], [ 3, 32, 33, 116, 281, 308, 342 ], [ 97, 98, 117, 132, 282, 309, 343 ], [ 5, 34, 35, 118, 283, 310, 336 ], [ 99, 100, 119, 134, 284, 311, 337 ], [ 15, 44, 45, 120, 229, 312, 346 ], [ 109, 110, 121, 136, 230, 313, 347 ], [ 9, 46, 47, 122, 231, 314, 348 ], [ 104, 111, 123, 138, 224, 315, 349 ], [ 11, 40, 41, 124, 225, 316, 350 ], [ 105, 106, 125, 140, 226, 317, 351 ], [ 13, 42, 43, 126, 227, 318, 344 ], [ 107, 108, 127, 142, 228, 319, 345 ], [ 23, 52, 53, 128, 320, 354, 365 ], [ 117, 118, 129, 144, 321, 355, 366 ], [ 17, 54, 55, 130, 322, 356, 367 ], [ 112, 119, 131, 146, 323, 357, 360 ], [ 19, 48, 49, 132, 324, 358, 361 ], [ 113, 114, 133, 148, 325, 359, 362 ], [ 21, 50, 51, 134, 326, 352, 363 ], [ 115, 116, 135, 150, 327, 353, 364 ], [ 31, 60, 61, 136, 309, 328, 362 ], [ 125, 126, 137, 152, 310, 329, 363 ], [ 25, 62, 63, 138, 311, 330, 364 ], [ 120, 127, 139, 154, 304, 331, 365 ], [ 27, 56, 57, 140, 305, 332, 366 ], [ 121, 122, 141, 156, 306, 333, 367 ], [ 29, 58, 59, 142, 307, 334, 360 ], [ 123, 124, 143, 158, 308, 335, 361 ], [ 39, 68, 69, 144, 253, 336, 370 ], [ 133, 134, 145, 160, 254, 337, 371 ], [ 33, 70, 71, 146, 255, 338, 372 ], [ 128, 135, 147, 162, 248, 339, 373 ], [ 35, 64, 65, 148, 249, 340, 374 ], [ 129, 130, 149, 164, 250, 341, 375 ], [ 37, 66, 67, 150, 251, 342, 368 ], [ 131, 132, 151, 166, 252, 343, 369 ], [ 47, 76, 77, 152, 197, 344, 378 ], [ 141, 142, 153, 168, 198, 345, 379 ], [ 41, 78, 79, 154, 199, 346, 380 ], [ 136, 143, 155, 170, 192, 347, 381 ], [ 43, 72, 73, 156, 193, 348, 382 ], [ 137, 138, 157, 172, 194, 349, 383 ], [ 45, 74, 75, 158, 195, 350, 376 ], [ 139, 140, 159, 174, 196, 351, 377 ], [ 55, 84, 85, 160, 194, 333, 352 ], [ 149, 150, 161, 176, 195, 334, 353 ], [ 49, 86, 87, 162, 196, 335, 354 ], [ 144, 151, 163, 178, 197, 328, 355 ], [ 51, 80, 81, 164, 198, 329, 356 ], [ 145, 146, 165, 180, 199, 330, 357 ], [ 53, 82, 83, 166, 192, 331, 358 ], [ 147, 148, 167, 182, 193, 332, 359 ], [ 63, 92, 93, 168, 202, 277, 360 ], [ 157, 158, 169, 184, 203, 278, 361 ], [ 57, 94, 95, 170, 204, 279, 362 ], [ 152, 159, 171, 186, 205, 272, 363 ], [ 59, 88, 89, 172, 206, 273, 364 ], [ 153, 154, 173, 188, 207, 274, 365 ], [ 61, 90, 91, 174, 200, 275, 366 ], [ 155, 156, 175, 190, 201, 276, 367 ], [ 71, 100, 101, 176, 210, 221, 368 ], [ 0, 165, 166, 177, 211, 222, 369 ], [ 65, 102, 103, 178, 212, 223, 370 ], [ 2, 160, 167, 179, 213, 216, 371 ], [ 67, 96, 97, 180, 214, 217, 372 ], [ 4, 161, 162, 181, 215, 218, 373 ], [ 69, 98, 99, 182, 208, 219, 374 ], [ 6, 163, 164, 183, 209, 220, 375 ], [ 79, 108, 109, 184, 218, 357, 376 ], [ 8, 173, 174, 185, 219, 358, 377 ], [ 73, 110, 111, 186, 220, 359, 378 ], [ 10, 168, 175, 187, 221, 352, 379 ], [ 75, 104, 105, 188, 222, 353, 380 ], [ 12, 169, 170, 189, 223, 354, 381 ], [ 77, 106, 107, 190, 216, 355, 382 ], [ 14, 171, 172, 191, 217, 356, 383 ] ] }, "distance": { "X": { "value": 23, "confidence": "upper_bound", "witness": [ 6, 24, 76, 108, 114, 152, 184, 194, 209, 228, 235, 240, 262, 278, 287, 315, 319, 325, 345, 349, 352, 363, 379 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 20000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 146614612, 1558732230 ], "survived_samples": 50000000 } }, "Z": { "value": 23, "confidence": "upper_bound", "witness": [ 0, 11, 20, 48, 52, 64, 82, 86, 93, 109, 112, 123, 143, 154, 169, 174, 211, 231, 243, 263, 275, 365, 377 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 50000000, "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)", "seeds": [ 146614612, 1558732230 ] } }, "d": 23 }, "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group-algebra code (Lin and Pryadko, arXiv:2306.16400) on G = C24:C8(r=17) of order 192, Cayley table research/kit/group_algebra.metacyclic(24, 8, 17) with the identity at index 0 and elements indexed as that builder lists them: H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] with L(g)[g h, h] = 1 and R(g)[h g, h] = 1 (research/kit/group_algebra.py build_2bga(mul, a, b)); a = [0, 34, 109], b = [0, 87, 116, 117] (element indices). n = 2|G| = 384, check weight 7.", "date": "2026-09-26", "notes": "Found by the third LER-objective search (weight-6 and weight-7 two-block codes at 300 < n <= 420 with k >= 12): circuit-level logical error rate at 3 rounds under the board's depolarizing recipe, interleaved schedule, decoded with CUDA-Q QEC nv-qldpc-decoder (BP+OSD-CS order 10). At p = 0.002, 100000 shots per basis: Z memory 18 failures, X memory 12 failures, against 16 copies of the distance-5 rotated surface code (784 physical qubits, same builder and decoder) with 1569 and 1716 failures. Decoder-based d_circ estimate at 3 rounds: 44. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. Details in the accompanying note.", "origin": "submission", "novelty": "unknown", "model": "Claude Fable 5.1 (Claude Code)" } }