{ "schema_version": "0.1", "name": "[[360,16,25]] CLP code, weight 7, SmallGroup(810,106)", "code_type": "CSS", "n": 360, "k": 16, "checks": { "X": [ [ 0, 33, 74, 180, 270, 314, 343 ], [ 1, 4, 87, 181, 271, 277, 319 ], [ 2, 48, 83, 182, 272, 329, 352 ], [ 3, 18, 84, 183, 273, 311, 331 ], [ 4, 9, 17, 184, 270, 274, 354 ], [ 5, 10, 89, 185, 275, 286, 333 ], [ 6, 25, 67, 186, 276, 288, 335 ], [ 0, 7, 30, 187, 277, 289, 336 ], [ 8, 61, 62, 188, 278, 330, 342 ], [ 9, 31, 88, 189, 279, 326, 344 ], [ 10, 20, 30, 190, 272, 280, 358 ], [ 7, 11, 59, 191, 281, 328, 345 ], [ 6, 12, 22, 192, 273, 282, 329 ], [ 13, 23, 81, 193, 274, 283, 292 ], [ 14, 21, 81, 194, 284, 299, 304 ], [ 15, 39, 78, 195, 285, 301, 346 ], [ 2, 16, 45, 196, 286, 302, 347 ], [ 12, 17, 80, 197, 287, 302, 303 ], [ 5, 11, 18, 198, 288, 304, 349 ], [ 19, 44, 48, 199, 289, 305, 350 ], [ 20, 46, 75, 200, 290, 297, 353 ], [ 3, 21, 45, 201, 278, 291, 345 ], [ 16, 22, 72, 202, 292, 341, 354 ], [ 15, 23, 36, 203, 279, 293, 342 ], [ 24, 37, 87, 204, 280, 294, 306 ], [ 1, 2, 25, 205, 281, 295, 344 ], [ 26, 39, 69, 206, 272, 282, 296 ], [ 27, 40, 68, 207, 283, 297, 309 ], [ 28, 53, 54, 208, 298, 316, 321 ], [ 8, 17, 29, 209, 299, 317, 322 ], [ 23, 30, 86, 210, 300, 317, 318 ], [ 14, 22, 31, 211, 301, 319, 355 ], [ 32, 59, 62, 212, 302, 320, 356 ], [ 3, 15, 33, 213, 303, 320, 321 ], [ 16, 34, 75, 214, 304, 322, 357 ], [ 27, 35, 65, 215, 285, 305, 323 ], [ 29, 36, 44, 216, 306, 313, 358 ], [ 11, 28, 37, 217, 290, 307, 314 ], [ 12, 38, 89, 218, 281, 291, 308 ], [ 5, 8, 39, 219, 292, 309, 353 ], [ 40, 54, 80, 220, 278, 293, 310 ], [ 41, 55, 79, 221, 294, 311, 324 ], [ 10, 42, 53, 222, 279, 295, 312 ], [ 43, 52, 57, 223, 280, 296, 313 ], [ 44, 51, 58, 224, 297, 314, 327 ], [ 37, 45, 69, 225, 289, 315, 332 ], [ 1, 36, 46, 226, 316, 333, 338 ], [ 33, 47, 72, 227, 317, 334, 339 ], [ 9, 28, 48, 228, 318, 334, 335 ], [ 29, 49, 84, 229, 319, 336, 359 ], [ 41, 50, 76, 230, 298, 320, 337 ], [ 31, 51, 61, 231, 321, 337, 338 ], [ 32, 52, 60, 232, 300, 322, 339 ], [ 13, 53, 79, 233, 271, 301, 323 ], [ 0, 14, 54, 234, 306, 324, 331 ], [ 25, 55, 86, 235, 270, 307, 325 ], [ 26, 56, 85, 236, 295, 308, 326 ], [ 21, 57, 67, 237, 290, 309, 327 ], [ 58, 66, 70, 238, 291, 310, 328 ], [ 59, 65, 71, 239, 311, 329, 340 ], [ 24, 35, 60, 240, 293, 312, 330 ], [ 34, 61, 73, 241, 294, 313, 331 ], [ 6, 20, 62, 242, 305, 332, 346 ], [ 7, 63, 88, 243, 333, 347, 351 ], [ 51, 56, 64, 244, 276, 334, 348 ], [ 46, 65, 74, 245, 335, 348, 349 ], [ 47, 66, 73, 246, 315, 336, 350 ], [ 24, 67, 85, 247, 275, 316, 337 ], [ 43, 49, 68, 248, 275, 338, 351 ], [ 42, 50, 69, 249, 276, 318, 339 ], [ 4, 70, 78, 250, 273, 324, 340 ], [ 42, 71, 77, 251, 274, 325, 341 ], [ 43, 72, 76, 252, 312, 326, 342 ], [ 38, 50, 73, 253, 307, 327, 343 ], [ 49, 74, 82, 254, 308, 328, 344 ], [ 19, 41, 75, 255, 310, 330, 345 ], [ 18, 76, 83, 256, 323, 346, 355 ], [ 19, 77, 82, 257, 287, 347, 356 ], [ 38, 68, 78, 258, 284, 288, 348 ], [ 58, 63, 79, 259, 284, 349, 357 ], [ 57, 64, 80, 260, 285, 332, 350 ], [ 26, 66, 81, 261, 286, 287, 351 ], [ 13, 64, 82, 262, 282, 340, 352 ], [ 60, 63, 83, 263, 283, 341, 353 ], [ 32, 56, 84, 264, 325, 343, 354 ], [ 34, 71, 85, 265, 271, 355, 359 ], [ 35, 70, 86, 266, 298, 303, 356 ], [ 40, 77, 87, 267, 299, 300, 357 ], [ 27, 47, 88, 268, 296, 352, 358 ], [ 52, 55, 89, 269, 277, 315, 359 ], [ 90, 123, 164, 180, 184, 237, 306 ], [ 91, 94, 177, 181, 233, 246, 298 ], [ 92, 138, 173, 182, 190, 250, 281 ], [ 93, 108, 174, 183, 192, 204, 278 ], [ 94, 99, 107, 184, 193, 253, 324 ], [ 95, 100, 179, 185, 247, 257, 276 ], [ 96, 115, 157, 186, 249, 259, 315 ], [ 90, 97, 120, 181, 187, 260, 316 ], [ 98, 151, 152, 188, 201, 222, 292 ], [ 99, 121, 178, 189, 203, 218, 270 ], [ 100, 110, 120, 190, 204, 262, 295 ], [ 97, 101, 149, 191, 205, 220, 290 ], [ 96, 102, 112, 192, 206, 221, 291 ], [ 103, 113, 171, 193, 207, 264, 340 ], [ 104, 111, 171, 194, 232, 258, 285 ], [ 105, 129, 168, 195, 260, 265, 287 ], [ 92, 106, 135, 185, 196, 266, 288 ], [ 102, 107, 170, 197, 230, 261, 284 ], [ 95, 101, 108, 186, 198, 267, 332 ], [ 109, 134, 138, 187, 195, 199, 333 ], [ 110, 136, 165, 193, 200, 217, 272 ], [ 93, 111, 135, 201, 218, 240, 309 ], [ 106, 112, 162, 202, 219, 235, 273 ], [ 105, 113, 126, 203, 220, 236, 274 ], [ 114, 127, 177, 204, 221, 268, 312 ], [ 91, 92, 115, 205, 222, 238, 307 ], [ 116, 129, 159, 206, 223, 239, 308 ], [ 117, 130, 158, 202, 207, 224, 352 ], [ 118, 143, 144, 208, 248, 266, 300 ], [ 98, 107, 119, 194, 209, 249, 301 ], [ 113, 120, 176, 210, 244, 267, 271 ], [ 104, 112, 121, 195, 211, 269, 303 ], [ 122, 149, 152, 196, 208, 212, 304 ], [ 93, 105, 123, 197, 213, 247, 299 ], [ 106, 124, 165, 198, 210, 214, 346 ], [ 117, 125, 155, 199, 211, 215, 347 ], [ 119, 126, 134, 206, 216, 234, 279 ], [ 101, 118, 127, 207, 217, 235, 280 ], [ 102, 128, 179, 218, 236, 255, 327 ], [ 95, 98, 129, 219, 237, 251, 282 ], [ 130, 144, 170, 220, 238, 252, 283 ], [ 131, 145, 169, 216, 221, 239, 330 ], [ 100, 132, 143, 222, 240, 254, 325 ], [ 133, 142, 147, 182, 223, 241, 326 ], [ 134, 141, 148, 180, 219, 224, 358 ], [ 127, 135, 159, 215, 225, 269, 275 ], [ 91, 126, 136, 208, 226, 261, 318 ], [ 123, 137, 162, 186, 209, 227, 319 ], [ 99, 118, 138, 210, 228, 258, 277 ], [ 119, 139, 174, 211, 225, 229, 321 ], [ 131, 140, 166, 212, 226, 230, 322 ], [ 121, 141, 151, 185, 213, 231, 317 ], [ 122, 142, 150, 214, 228, 232, 355 ], [ 103, 143, 169, 215, 229, 233, 356 ], [ 90, 104, 144, 223, 234, 250, 293 ], [ 115, 145, 176, 224, 235, 251, 294 ], [ 116, 146, 175, 191, 236, 252, 343 ], [ 111, 147, 157, 237, 253, 263, 296 ], [ 148, 156, 160, 188, 238, 254, 297 ], [ 149, 155, 161, 182, 234, 239, 345 ], [ 114, 125, 150, 189, 240, 255, 341 ], [ 124, 151, 163, 183, 190, 241, 342 ], [ 96, 110, 152, 225, 233, 242, 286 ], [ 97, 153, 178, 197, 226, 243, 335 ], [ 141, 146, 154, 198, 227, 244, 336 ], [ 136, 155, 164, 194, 228, 245, 289 ], [ 137, 156, 163, 229, 242, 246, 338 ], [ 114, 157, 175, 230, 243, 247, 339 ], [ 133, 139, 158, 196, 231, 248, 334 ], [ 132, 140, 159, 232, 245, 249, 359 ], [ 94, 160, 168, 241, 250, 262, 310 ], [ 132, 161, 167, 180, 251, 263, 311 ], [ 133, 162, 166, 188, 205, 252, 354 ], [ 128, 140, 163, 200, 253, 264, 313 ], [ 139, 164, 172, 189, 201, 254, 314 ], [ 109, 131, 165, 191, 203, 255, 353 ], [ 108, 166, 173, 181, 242, 256, 302 ], [ 109, 167, 172, 213, 243, 257, 349 ], [ 128, 158, 168, 214, 244, 258, 350 ], [ 148, 153, 169, 209, 245, 259, 305 ], [ 147, 154, 170, 246, 256, 260, 351 ], [ 116, 156, 171, 212, 248, 261, 348 ], [ 103, 154, 172, 183, 262, 268, 328 ], [ 150, 153, 173, 184, 200, 263, 329 ], [ 122, 146, 174, 202, 217, 264, 331 ], [ 124, 161, 175, 187, 256, 265, 320 ], [ 125, 160, 176, 231, 257, 266, 357 ], [ 130, 167, 177, 227, 259, 267, 323 ], [ 117, 137, 178, 192, 216, 268, 344 ], [ 142, 145, 179, 199, 265, 269, 337 ] ], "Z": [ [ 0, 90, 134, 161, 180, 187, 234 ], [ 1, 91, 97, 166, 181, 205, 226 ], [ 2, 92, 133, 149, 182, 196, 205 ], [ 3, 93, 151, 172, 183, 201, 213 ], [ 4, 90, 94, 173, 181, 184, 250 ], [ 5, 95, 106, 141, 185, 198, 219 ], [ 6, 96, 108, 137, 186, 192, 242 ], [ 7, 97, 109, 175, 187, 191, 243 ], [ 8, 98, 148, 162, 188, 209, 219 ], [ 9, 99, 150, 164, 184, 189, 228 ], [ 10, 92, 100, 151, 185, 190, 222 ], [ 11, 101, 146, 165, 191, 198, 217 ], [ 12, 93, 102, 178, 192, 197, 218 ], [ 13, 94, 103, 110, 193, 233, 262 ], [ 14, 104, 119, 155, 194, 211, 234 ], [ 15, 105, 109, 121, 195, 203, 213 ], [ 16, 106, 122, 158, 196, 202, 214 ], [ 17, 107, 123, 153, 184, 197, 209 ], [ 18, 108, 124, 154, 183, 198, 256 ], [ 19, 109, 125, 179, 199, 255, 257 ], [ 20, 110, 163, 173, 190, 200, 242 ], [ 21, 98, 111, 164, 194, 201, 237 ], [ 22, 112, 117, 174, 192, 202, 211 ], [ 23, 99, 113, 165, 193, 203, 210 ], [ 24, 93, 100, 114, 204, 240, 247 ], [ 25, 101, 115, 162, 186, 205, 235 ], [ 26, 102, 116, 126, 206, 236, 261 ], [ 27, 103, 117, 127, 207, 215, 268 ], [ 28, 118, 122, 136, 208, 217, 228 ], [ 29, 119, 137, 169, 209, 216, 229 ], [ 30, 120, 124, 138, 187, 190, 210 ], [ 31, 121, 125, 139, 189, 211, 231 ], [ 32, 122, 140, 171, 212, 232, 264 ], [ 33, 123, 141, 167, 180, 213, 227 ], [ 34, 124, 142, 168, 214, 241, 265 ], [ 35, 125, 135, 143, 215, 240, 266 ], [ 36, 126, 131, 178, 203, 216, 226 ], [ 37, 110, 127, 174, 204, 217, 225 ], [ 38, 99, 111, 128, 218, 253, 258 ], [ 39, 112, 129, 134, 195, 206, 219 ], [ 40, 101, 113, 130, 207, 220, 267 ], [ 41, 102, 114, 131, 221, 230, 255 ], [ 42, 98, 115, 132, 222, 249, 251 ], [ 43, 116, 133, 144, 223, 248, 252 ], [ 44, 117, 134, 145, 199, 216, 224 ], [ 45, 135, 139, 152, 196, 201, 225 ], [ 46, 136, 140, 153, 200, 226, 245 ], [ 47, 137, 154, 177, 227, 246, 268 ], [ 48, 138, 142, 155, 182, 199, 228 ], [ 49, 139, 143, 156, 229, 248, 254 ], [ 50, 107, 140, 157, 230, 249, 253 ], [ 51, 141, 158, 176, 224, 231, 244 ], [ 52, 104, 142, 159, 223, 232, 269 ], [ 53, 91, 143, 152, 208, 222, 233 ], [ 54, 126, 144, 149, 208, 220, 234 ], [ 55, 112, 127, 145, 221, 235, 269 ], [ 56, 113, 128, 146, 236, 244, 264 ], [ 57, 90, 129, 147, 223, 237, 260 ], [ 58, 115, 130, 148, 224, 238, 259 ], [ 59, 116, 131, 149, 191, 212, 239 ], [ 60, 111, 132, 150, 232, 240, 263 ], [ 61, 133, 151, 160, 188, 231, 241 ], [ 62, 152, 156, 166, 188, 212, 242 ], [ 63, 153, 157, 167, 243, 259, 263 ], [ 64, 120, 154, 168, 244, 260, 262 ], [ 65, 155, 159, 169, 215, 239, 245 ], [ 66, 91, 156, 170, 238, 246, 261 ], [ 67, 95, 123, 157, 186, 237, 247 ], [ 68, 118, 158, 171, 207, 248, 258 ], [ 69, 96, 119, 159, 206, 225, 249 ], [ 70, 92, 144, 160, 238, 250, 266 ], [ 71, 129, 145, 161, 239, 251, 265 ], [ 72, 130, 146, 162, 202, 227, 252 ], [ 73, 94, 147, 163, 241, 246, 253 ], [ 74, 132, 148, 164, 180, 245, 254 ], [ 75, 128, 150, 165, 200, 214, 255 ], [ 76, 166, 170, 175, 230, 252, 256 ], [ 77, 95, 167, 176, 251, 257, 267 ], [ 78, 104, 138, 168, 195, 250, 258 ], [ 79, 96, 169, 177, 221, 233, 259 ], [ 80, 97, 105, 170, 197, 220, 260 ], [ 81, 107, 136, 171, 193, 194, 261 ], [ 82, 100, 160, 172, 254, 257, 262 ], [ 83, 147, 161, 173, 182, 256, 263 ], [ 84, 103, 163, 174, 183, 229, 264 ], [ 85, 105, 175, 179, 236, 247, 265 ], [ 86, 106, 118, 176, 210, 235, 266 ], [ 87, 108, 120, 177, 181, 204, 267 ], [ 88, 114, 172, 178, 189, 243, 268 ], [ 89, 121, 135, 179, 185, 218, 269 ], [ 0, 4, 55, 99, 270, 277, 324 ], [ 1, 53, 85, 120, 271, 295, 316 ], [ 2, 10, 26, 110, 272, 286, 295 ], [ 3, 12, 70, 112, 273, 291, 303 ], [ 4, 13, 71, 113, 271, 274, 340 ], [ 5, 67, 68, 135, 275, 288, 309 ], [ 6, 64, 69, 95, 276, 282, 332 ], [ 1, 7, 89, 138, 277, 281, 333 ], [ 8, 21, 40, 93, 278, 299, 309 ], [ 9, 23, 42, 126, 274, 279, 318 ], [ 10, 24, 43, 127, 275, 280, 312 ], [ 11, 25, 38, 92, 281, 288, 307 ], [ 12, 26, 82, 129, 282, 287, 308 ], [ 13, 27, 83, 130, 283, 323, 352 ], [ 14, 78, 79, 107, 284, 301, 324 ], [ 15, 35, 80, 104, 285, 293, 303 ], [ 5, 16, 81, 152, 286, 292, 304 ], [ 17, 77, 81, 105, 274, 287, 299 ], [ 6, 18, 78, 106, 273, 288, 346 ], [ 7, 19, 45, 155, 289, 345, 347 ], [ 20, 37, 57, 101, 280, 290, 332 ], [ 21, 38, 58, 102, 284, 291, 327 ], [ 13, 22, 39, 98, 282, 292, 301 ], [ 23, 40, 60, 144, 283, 293, 300 ], [ 24, 41, 61, 145, 294, 330, 337 ], [ 25, 42, 56, 100, 276, 295, 325 ], [ 26, 43, 88, 147, 296, 326, 351 ], [ 20, 27, 44, 148, 297, 305, 358 ], [ 28, 50, 86, 91, 298, 307, 318 ], [ 14, 29, 87, 123, 299, 306, 319 ], [ 30, 52, 87, 118, 277, 280, 300 ], [ 15, 31, 53, 119, 279, 301, 321 ], [ 16, 17, 32, 166, 302, 322, 354 ], [ 17, 33, 86, 121, 270, 303, 317 ], [ 14, 18, 34, 122, 304, 331, 355 ], [ 19, 35, 62, 169, 305, 330, 356 ], [ 24, 36, 54, 90, 293, 306, 316 ], [ 37, 55, 73, 115, 294, 307, 315 ], [ 38, 56, 74, 116, 308, 343, 348 ], [ 27, 39, 57, 111, 285, 296, 309 ], [ 40, 58, 75, 160, 297, 310, 357 ], [ 3, 41, 59, 161, 311, 320, 345 ], [ 42, 60, 72, 114, 312, 339, 341 ], [ 36, 43, 61, 163, 313, 338, 342 ], [ 0, 37, 44, 164, 289, 306, 314 ], [ 45, 66, 89, 96, 286, 291, 315 ], [ 28, 46, 67, 97, 290, 316, 335 ], [ 29, 30, 47, 141, 317, 336, 358 ], [ 30, 48, 69, 136, 272, 289, 318 ], [ 1, 31, 49, 137, 319, 338, 344 ], [ 32, 33, 50, 175, 320, 339, 343 ], [ 28, 33, 51, 139, 314, 321, 334 ], [ 29, 34, 52, 140, 313, 322, 359 ], [ 35, 53, 76, 177, 298, 312, 323 ], [ 41, 54, 70, 94, 298, 310, 324 ], [ 55, 71, 84, 132, 311, 325, 359 ], [ 9, 56, 72, 133, 326, 334, 354 ], [ 44, 57, 73, 128, 313, 327, 350 ], [ 11, 58, 74, 172, 314, 328, 349 ], [ 2, 12, 59, 173, 281, 302, 329 ], [ 8, 60, 75, 131, 322, 330, 353 ], [ 3, 54, 61, 174, 278, 321, 331 ], [ 45, 62, 80, 108, 278, 302, 332 ], [ 5, 46, 63, 109, 333, 349, 353 ], [ 47, 48, 64, 158, 334, 350, 352 ], [ 6, 48, 65, 153, 305, 329, 335 ], [ 7, 49, 66, 154, 328, 336, 351 ], [ 50, 51, 67, 179, 276, 327, 337 ], [ 46, 51, 68, 156, 297, 338, 348 ], [ 47, 52, 69, 157, 296, 315, 339 ], [ 59, 70, 82, 103, 328, 340, 356 ], [ 22, 71, 83, 150, 329, 341, 355 ], [ 8, 23, 72, 151, 292, 317, 342 ], [ 0, 73, 84, 146, 331, 336, 343 ], [ 9, 25, 74, 178, 270, 335, 344 ], [ 11, 21, 75, 149, 290, 304, 345 ], [ 15, 62, 76, 124, 320, 342, 346 ], [ 16, 63, 77, 125, 341, 347, 357 ], [ 64, 65, 78, 171, 285, 340, 348 ], [ 18, 65, 79, 167, 311, 323, 349 ], [ 19, 66, 80, 168, 287, 310, 350 ], [ 63, 68, 81, 170, 283, 284, 351 ], [ 2, 82, 88, 117, 344, 347, 352 ], [ 20, 39, 83, 165, 272, 346, 353 ], [ 4, 22, 84, 162, 273, 319, 354 ], [ 31, 76, 85, 142, 326, 337, 355 ], [ 32, 77, 86, 143, 300, 325, 356 ], [ 34, 79, 87, 176, 271, 294, 357 ], [ 10, 36, 88, 134, 279, 333, 358 ], [ 49, 85, 89, 159, 275, 308, 359 ] ] }, "distance": { "d": 25, "X": { "value": 25, "confidence": "upper_bound", "witness": [ 25, 51, 92, 95, 139, 156, 178, 181, 185, 186, 196, 200, 207, 214, 218, 226, 231, 241, 242, 246, 250, 258, 267, 268, 276 ] }, "Z": { "value": 26, "confidence": "upper_bound", "witness": [ 7, 36, 97, 100, 106, 116, 124, 137, 151, 156, 162, 178, 185, 187, 188, 191, 216, 218, 240, 255, 279, 295, 308, 330, 333, 344 ] } }, "provenance": { "authors": [ "@rajendrarajpurohit" ], "construction": "Coset lifted product (CLP) code, Definition III.1 of arXiv:2610.12782, 1x1 over 2x2 layout, check weight 7. G = SmallGroup(810,106) (GAP SmallGroups id), H = = C3 x C3 by generators in the polycyclic generating sequence f1,f2,... of G, m = [G:H] = 90, n = 4m = 360. a over F_2[G] by the left coset action on G/H, B over F_2[N_G(H)] by the right coset action. a = 1 + f1*f3*f5*f6 + f3^2*f4*f6^4; B = [[1, 1 + f6^4 + f4*f5^2*f6^3], [1 + f6 + f4*f5^2*f6^2, f4^2*f5^2]]. Rebuild with gap/rebuild.g in https://github.com/rajendrarajpurohit/CLP_QLDPC.", "origin": "submission", "date": "2026-11-03", "references": [ "arXiv:2610.12782" ], "novelty": "known_parameters", "notes": "Table II of arXiv:2610.12782 lists this code with the two sided QDistRnd bound d <= 25 at 10^6 rounds; the witness here is from this tool's own search and the entry carries that value. Authors Rajendra Rajpurohit, V. Lalitha, Shayan Srinivasa Garani.", "model": "human" }, "family": "2bga-coset" }