{ "schema_version": "0.1", "name": "[[360,80,4]] [[4,2,2]]-amplified [[80,40,2]] 2BGA", "code_type": "CSS", "n": 360, "k": 80, "checks": { "X": [ [ 0, 16, 160, 176, 300, 316, 340 ], [ 1, 17, 161, 177, 301, 317, 340 ], [ 2, 18, 162, 178, 302, 318, 340 ], [ 3, 19, 163, 179, 303, 319, 340 ], [ 48, 88, 168, 200, 208, 248, 341 ], [ 49, 89, 169, 201, 209, 249, 341 ], [ 50, 90, 170, 202, 210, 250, 341 ], [ 51, 91, 171, 203, 211, 251, 341 ], [ 52, 92, 172, 204, 212, 252, 342 ], [ 53, 93, 173, 205, 213, 253, 342 ], [ 54, 94, 174, 206, 214, 254, 342 ], [ 55, 95, 175, 207, 215, 255, 342 ], [ 96, 132, 256, 276, 292, 308, 343 ], [ 97, 133, 257, 277, 293, 309, 343 ], [ 98, 134, 258, 278, 294, 310, 343 ], [ 99, 135, 259, 279, 295, 311, 343 ], [ 100, 136, 208, 248, 260, 296, 344 ], [ 101, 137, 209, 249, 261, 297, 344 ], [ 102, 138, 210, 250, 262, 298, 344 ], [ 103, 139, 211, 251, 263, 299, 344 ], [ 64, 104, 224, 244, 264, 284, 345 ], [ 65, 105, 225, 245, 265, 285, 345 ], [ 66, 106, 226, 246, 266, 286, 345 ], [ 67, 107, 227, 247, 267, 287, 345 ], [ 68, 108, 180, 216, 228, 268, 346 ], [ 69, 109, 181, 217, 229, 269, 346 ], [ 70, 110, 182, 218, 230, 270, 346 ], [ 71, 111, 183, 219, 231, 271, 346 ], [ 112, 144, 224, 264, 272, 304, 347 ], [ 113, 145, 225, 265, 273, 305, 347 ], [ 114, 146, 226, 266, 274, 306, 347 ], [ 115, 147, 227, 267, 275, 307, 347 ], [ 84, 124, 196, 236, 244, 284, 348 ], [ 85, 125, 197, 237, 245, 285, 348 ], [ 86, 126, 198, 238, 246, 286, 348 ], [ 87, 127, 199, 239, 247, 287, 348 ], [ 116, 148, 228, 268, 276, 308, 349 ], [ 117, 149, 229, 269, 277, 309, 349 ], [ 118, 150, 230, 270, 278, 310, 349 ], [ 119, 151, 231, 271, 279, 311, 349 ], [ 128, 152, 240, 280, 288, 312, 350 ], [ 129, 153, 241, 281, 289, 313, 350 ], [ 130, 154, 242, 282, 290, 314, 350 ], [ 131, 155, 243, 283, 291, 315, 350 ], [ 140, 156, 260, 296, 300, 316, 351 ], [ 141, 157, 261, 297, 301, 317, 351 ], [ 142, 158, 262, 298, 302, 318, 351 ], [ 143, 159, 263, 299, 303, 319, 351 ], [ 80, 120, 192, 232, 240, 280, 352 ], [ 81, 121, 193, 233, 241, 281, 352 ], [ 82, 122, 194, 234, 242, 282, 352 ], [ 83, 123, 195, 235, 243, 283, 352 ], [ 36, 76, 164, 188, 196, 236, 353 ], [ 37, 77, 165, 189, 197, 237, 353 ], [ 38, 78, 166, 190, 198, 238, 353 ], [ 39, 79, 167, 191, 199, 239, 353 ], [ 32, 72, 192, 212, 232, 252, 354 ], [ 33, 73, 193, 213, 233, 253, 354 ], [ 34, 74, 194, 214, 234, 254, 354 ], [ 35, 75, 195, 215, 235, 255, 354 ], [ 4, 28, 164, 188, 256, 292, 355 ], [ 5, 29, 165, 189, 257, 293, 355 ], [ 6, 30, 166, 190, 258, 294, 355 ], [ 7, 31, 167, 191, 259, 295, 355 ], [ 8, 40, 168, 184, 200, 220, 356 ], [ 9, 41, 169, 185, 201, 221, 356 ], [ 10, 42, 170, 186, 202, 222, 356 ], [ 11, 43, 171, 187, 203, 223, 356 ], [ 12, 44, 172, 204, 272, 304, 357 ], [ 13, 45, 173, 205, 273, 305, 357 ], [ 14, 46, 174, 206, 274, 306, 357 ], [ 15, 47, 175, 207, 275, 307, 357 ], [ 20, 56, 160, 176, 180, 216, 358 ], [ 21, 57, 161, 177, 181, 217, 358 ], [ 22, 58, 162, 178, 182, 218, 358 ], [ 23, 59, 163, 179, 183, 219, 358 ], [ 24, 60, 184, 220, 288, 312, 359 ], [ 25, 61, 185, 221, 289, 313, 359 ], [ 26, 62, 186, 222, 290, 314, 359 ], [ 27, 63, 187, 223, 291, 315, 359 ], [ 0, 1, 2, 3, 320, 331 ], [ 4, 5, 6, 7, 323, 335 ], [ 8, 9, 10, 11, 336, 339 ], [ 12, 13, 14, 15, 327, 337 ], [ 16, 17, 18, 19, 320, 331 ], [ 20, 21, 22, 23, 320, 338 ], [ 24, 25, 26, 27, 330, 339 ], [ 28, 29, 30, 31, 323, 335 ], [ 32, 33, 34, 35, 322, 334 ], [ 36, 37, 38, 39, 333, 335 ], [ 40, 41, 42, 43, 336, 339 ], [ 44, 45, 46, 47, 327, 337 ], [ 48, 49, 50, 51, 321, 336 ], [ 52, 53, 54, 55, 322, 337 ], [ 56, 57, 58, 59, 320, 338 ], [ 60, 61, 62, 63, 330, 339 ], [ 64, 65, 66, 67, 325, 328 ], [ 68, 69, 70, 71, 326, 338 ], [ 72, 73, 74, 75, 322, 334 ], [ 76, 77, 78, 79, 333, 335 ], [ 80, 81, 82, 83, 332, 334 ], [ 84, 85, 86, 87, 328, 333 ], [ 88, 89, 90, 91, 321, 336 ], [ 92, 93, 94, 95, 322, 337 ], [ 96, 97, 98, 99, 323, 329 ], [ 100, 101, 102, 103, 321, 324 ], [ 104, 105, 106, 107, 325, 328 ], [ 108, 109, 110, 111, 326, 338 ], [ 112, 113, 114, 115, 325, 327 ], [ 116, 117, 118, 119, 326, 329 ], [ 120, 121, 122, 123, 332, 334 ], [ 124, 125, 126, 127, 328, 333 ], [ 128, 129, 130, 131, 330, 332 ], [ 132, 133, 134, 135, 323, 329 ], [ 136, 137, 138, 139, 321, 324 ], [ 140, 141, 142, 143, 324, 331 ], [ 144, 145, 146, 147, 325, 327 ], [ 148, 149, 150, 151, 326, 329 ], [ 152, 153, 154, 155, 330, 332 ], [ 156, 157, 158, 159, 324, 331 ], [ 160, 161, 162, 163, 320 ], [ 164, 165, 166, 167, 335 ], [ 168, 169, 170, 171, 336 ], [ 172, 173, 174, 175, 337 ], [ 176, 177, 178, 179, 320 ], [ 180, 181, 182, 183, 338 ], [ 184, 185, 186, 187, 339 ], [ 188, 189, 190, 191, 335 ], [ 192, 193, 194, 195, 334 ], [ 196, 197, 198, 199, 333 ], [ 200, 201, 202, 203, 336 ], [ 204, 205, 206, 207, 337 ], [ 208, 209, 210, 211, 321 ], [ 212, 213, 214, 215, 322 ], [ 216, 217, 218, 219, 338 ], [ 220, 221, 222, 223, 339 ], [ 224, 225, 226, 227, 325 ], [ 228, 229, 230, 231, 326 ], [ 232, 233, 234, 235, 334 ], [ 236, 237, 238, 239, 333 ], [ 240, 241, 242, 243, 332 ], [ 244, 245, 246, 247, 328 ], [ 248, 249, 250, 251, 321 ], [ 252, 253, 254, 255, 322 ], [ 256, 257, 258, 259, 323 ], [ 260, 261, 262, 263, 324 ], [ 264, 265, 266, 267, 325 ], [ 268, 269, 270, 271, 326 ], [ 272, 273, 274, 275, 327 ], [ 276, 277, 278, 279, 329 ], [ 280, 281, 282, 283, 332 ], [ 284, 285, 286, 287, 328 ], [ 288, 289, 290, 291, 330 ], [ 292, 293, 294, 295, 323 ], [ 296, 297, 298, 299, 324 ], [ 300, 301, 302, 303, 331 ], [ 304, 305, 306, 307, 327 ], [ 308, 309, 310, 311, 329 ], [ 312, 313, 314, 315, 330 ], [ 316, 317, 318, 319, 331 ] ], "Z": [ [ 0, 16, 20, 56, 160, 176, 320 ], [ 1, 17, 21, 57, 161, 177, 320 ], [ 2, 18, 22, 58, 162, 178, 320 ], [ 3, 19, 23, 59, 163, 179, 320 ], [ 48, 88, 100, 136, 208, 248, 321 ], [ 49, 89, 101, 137, 209, 249, 321 ], [ 50, 90, 102, 138, 210, 250, 321 ], [ 51, 91, 103, 139, 211, 251, 321 ], [ 32, 52, 72, 92, 212, 252, 322 ], [ 33, 53, 73, 93, 213, 253, 322 ], [ 34, 54, 74, 94, 214, 254, 322 ], [ 35, 55, 75, 95, 215, 255, 322 ], [ 4, 28, 96, 132, 256, 292, 323 ], [ 5, 29, 97, 133, 257, 293, 323 ], [ 6, 30, 98, 134, 258, 294, 323 ], [ 7, 31, 99, 135, 259, 295, 323 ], [ 100, 136, 140, 156, 260, 296, 324 ], [ 101, 137, 141, 157, 261, 297, 324 ], [ 102, 138, 142, 158, 262, 298, 324 ], [ 103, 139, 143, 159, 263, 299, 324 ], [ 64, 104, 112, 144, 224, 264, 325 ], [ 65, 105, 113, 145, 225, 265, 325 ], [ 66, 106, 114, 146, 226, 266, 325 ], [ 67, 107, 115, 147, 227, 267, 325 ], [ 68, 108, 116, 148, 228, 268, 326 ], [ 69, 109, 117, 149, 229, 269, 326 ], [ 70, 110, 118, 150, 230, 270, 326 ], [ 71, 111, 119, 151, 231, 271, 326 ], [ 12, 44, 112, 144, 272, 304, 327 ], [ 13, 45, 113, 145, 273, 305, 327 ], [ 14, 46, 114, 146, 274, 306, 327 ], [ 15, 47, 115, 147, 275, 307, 327 ], [ 64, 84, 104, 124, 244, 284, 328 ], [ 65, 85, 105, 125, 245, 285, 328 ], [ 66, 86, 106, 126, 246, 286, 328 ], [ 67, 87, 107, 127, 247, 287, 328 ], [ 96, 116, 132, 148, 276, 308, 329 ], [ 97, 117, 133, 149, 277, 309, 329 ], [ 98, 118, 134, 150, 278, 310, 329 ], [ 99, 119, 135, 151, 279, 311, 329 ], [ 24, 60, 128, 152, 288, 312, 330 ], [ 25, 61, 129, 153, 289, 313, 330 ], [ 26, 62, 130, 154, 290, 314, 330 ], [ 27, 63, 131, 155, 291, 315, 330 ], [ 0, 16, 140, 156, 300, 316, 331 ], [ 1, 17, 141, 157, 301, 317, 331 ], [ 2, 18, 142, 158, 302, 318, 331 ], [ 3, 19, 143, 159, 303, 319, 331 ], [ 80, 120, 128, 152, 240, 280, 332 ], [ 81, 121, 129, 153, 241, 281, 332 ], [ 82, 122, 130, 154, 242, 282, 332 ], [ 83, 123, 131, 155, 243, 283, 332 ], [ 36, 76, 84, 124, 196, 236, 333 ], [ 37, 77, 85, 125, 197, 237, 333 ], [ 38, 78, 86, 126, 198, 238, 333 ], [ 39, 79, 87, 127, 199, 239, 333 ], [ 32, 72, 80, 120, 192, 232, 334 ], [ 33, 73, 81, 121, 193, 233, 334 ], [ 34, 74, 82, 122, 194, 234, 334 ], [ 35, 75, 83, 123, 195, 235, 334 ], [ 4, 28, 36, 76, 164, 188, 335 ], [ 5, 29, 37, 77, 165, 189, 335 ], [ 6, 30, 38, 78, 166, 190, 335 ], [ 7, 31, 39, 79, 167, 191, 335 ], [ 8, 40, 48, 88, 168, 200, 336 ], [ 9, 41, 49, 89, 169, 201, 336 ], [ 10, 42, 50, 90, 170, 202, 336 ], [ 11, 43, 51, 91, 171, 203, 336 ], [ 12, 44, 52, 92, 172, 204, 337 ], [ 13, 45, 53, 93, 173, 205, 337 ], [ 14, 46, 54, 94, 174, 206, 337 ], [ 15, 47, 55, 95, 175, 207, 337 ], [ 20, 56, 68, 108, 180, 216, 338 ], [ 21, 57, 69, 109, 181, 217, 338 ], [ 22, 58, 70, 110, 182, 218, 338 ], [ 23, 59, 71, 111, 183, 219, 338 ], [ 8, 24, 40, 60, 184, 220, 339 ], [ 9, 25, 41, 61, 185, 221, 339 ], [ 10, 26, 42, 62, 186, 222, 339 ], [ 11, 27, 43, 63, 187, 223, 339 ], [ 0, 1, 2, 3, 340 ], [ 4, 5, 6, 7, 355 ], [ 8, 9, 10, 11, 356 ], [ 12, 13, 14, 15, 357 ], [ 16, 17, 18, 19, 340 ], [ 20, 21, 22, 23, 358 ], [ 24, 25, 26, 27, 359 ], [ 28, 29, 30, 31, 355 ], [ 32, 33, 34, 35, 354 ], [ 36, 37, 38, 39, 353 ], [ 40, 41, 42, 43, 356 ], [ 44, 45, 46, 47, 357 ], [ 48, 49, 50, 51, 341 ], [ 52, 53, 54, 55, 342 ], [ 56, 57, 58, 59, 358 ], [ 60, 61, 62, 63, 359 ], [ 64, 65, 66, 67, 345 ], [ 68, 69, 70, 71, 346 ], [ 72, 73, 74, 75, 354 ], [ 76, 77, 78, 79, 353 ], [ 80, 81, 82, 83, 352 ], [ 84, 85, 86, 87, 348 ], [ 88, 89, 90, 91, 341 ], [ 92, 93, 94, 95, 342 ], [ 96, 97, 98, 99, 343 ], [ 100, 101, 102, 103, 344 ], [ 104, 105, 106, 107, 345 ], [ 108, 109, 110, 111, 346 ], [ 112, 113, 114, 115, 347 ], [ 116, 117, 118, 119, 349 ], [ 120, 121, 122, 123, 352 ], [ 124, 125, 126, 127, 348 ], [ 128, 129, 130, 131, 350 ], [ 132, 133, 134, 135, 343 ], [ 136, 137, 138, 139, 344 ], [ 140, 141, 142, 143, 351 ], [ 144, 145, 146, 147, 347 ], [ 148, 149, 150, 151, 349 ], [ 152, 153, 154, 155, 350 ], [ 156, 157, 158, 159, 351 ], [ 160, 161, 162, 163, 340, 358 ], [ 164, 165, 166, 167, 353, 355 ], [ 168, 169, 170, 171, 341, 356 ], [ 172, 173, 174, 175, 342, 357 ], [ 176, 177, 178, 179, 340, 358 ], [ 180, 181, 182, 183, 346, 358 ], [ 184, 185, 186, 187, 356, 359 ], [ 188, 189, 190, 191, 353, 355 ], [ 192, 193, 194, 195, 352, 354 ], [ 196, 197, 198, 199, 348, 353 ], [ 200, 201, 202, 203, 341, 356 ], [ 204, 205, 206, 207, 342, 357 ], [ 208, 209, 210, 211, 341, 344 ], [ 212, 213, 214, 215, 342, 354 ], [ 216, 217, 218, 219, 346, 358 ], [ 220, 221, 222, 223, 356, 359 ], [ 224, 225, 226, 227, 345, 347 ], [ 228, 229, 230, 231, 346, 349 ], [ 232, 233, 234, 235, 352, 354 ], [ 236, 237, 238, 239, 348, 353 ], [ 240, 241, 242, 243, 350, 352 ], [ 244, 245, 246, 247, 345, 348 ], [ 248, 249, 250, 251, 341, 344 ], [ 252, 253, 254, 255, 342, 354 ], [ 256, 257, 258, 259, 343, 355 ], [ 260, 261, 262, 263, 344, 351 ], [ 264, 265, 266, 267, 345, 347 ], [ 268, 269, 270, 271, 346, 349 ], [ 272, 273, 274, 275, 347, 357 ], [ 276, 277, 278, 279, 343, 349 ], [ 280, 281, 282, 283, 350, 352 ], [ 284, 285, 286, 287, 345, 348 ], [ 288, 289, 290, 291, 350, 359 ], [ 292, 293, 294, 295, 343, 355 ], [ 296, 297, 298, 299, 344, 351 ], [ 300, 301, 302, 303, 340, 351 ], [ 304, 305, 306, 307, 347, 357 ], [ 308, 309, 310, 311, 343, 349 ], [ 312, 313, 314, 315, 350, 359 ], [ 316, 317, 318, 319, 340, 351 ] ] }, "distance": { "d": 4, "X": { "value": 4, "confidence": "upper_bound", "witness": [ 172, 173, 204, 205 ] }, "Z": { "value": 4, "confidence": "upper_bound", "witness": [ 12, 13, 44, 45 ] } }, "provenance": { "authors": [ "@MathysRennela" ], "construction": "Distance-amplified code: one [[4,2,2]] tensor-product amplification step (central three-term truncation of the chain-complex tensor product, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[80,40,2]] 2BGA entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 360, k' = 2k = 80, check weight w' = w+1 = 7. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 4/4); a 100000-trial fast-backend search (seed 5000) found nothing lighter (min weight 4). Base provenance: 2BGA (arXiv:2306.16400) on SmallGroup(40,2), from github.com/QEC-pages/2BGA-codes @ 403d194c3f98f0cadc236aecbc4a8b6139ccf23c, abelian.zip, diswtabelian_wt6wtL2_order40_k40.txt, line 1. nonidentity supports a=[5], b=[5, 6, 15].", "references": [ "arXiv:2609.37231" ], "date": "2026-09-30", "notes": "Constructed and packaged with the Space Bunny Alpha 1.0 model.", "model": "Space Bunny Alpha 1.0" }, "family": "distance-amplified" }