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[[360,38,8]] d ≤
n
360
k
38
d
8
kd²/n
6.756
w
5
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 8, d_Z ≤ 8 · w_X = 5, w_Z = 4 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[53, 85, 86, 143, 212, 217, 259, 298]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[33, 58, 110, 155, 258, 306, 320, 336]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 8 · H_Z 10 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 5 · H_Z 4
qubit degrees H_X 2 · H_Z 2
trapping sets H_X (1,2)×360 (2,2)×1440 (3,2)×5760 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 360 (2,2): 1440 (3,2): 5760 (3,4): 1440
trapping sets H_Z (1,2)×360 (2,2)×1080 (3,2)×3240 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 360 (2,2): 1080 (3,2): 3240 (3,4): 720

Construction & provenance

authors @msilve160
provenance submitted through the challenge
novelty novelty not audited
construction Planar hyperbolic {4,5} code, literature reproduction from github.com/QEC-pages/Quantum_LDPC_Codes @ 1c95489383564e4dc2cce517de00d64d6f2c4f56, Hyperbolic_Codes_Planar.zip, N=360. Same source repository already used for codes/720-122-8.json etc (Seam D); this pulls a different (p,q,N) entry from the same pinned catalog. CSS code, edge model.
model Claude Claude Sonnet 5 (claimed, not verified)
builds on github.com/QEC-pages/Quantum_LDPC_Codes
date 2026-09-19
family topological (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[360,38,8]] — planar hyperbolic {4,5} code

Credit

Literature reproduction, not an original construction: matrices come unmodified from github.com/QEC-pages/Quantum_LDPC_Codes @ 1c95489383564e4dc2cce517de00d64d6f2c4f56 (Hyperbolic_Codes_Planar.zip), the same pinned source @MathysRennela (using DeepSeek V4 Flash 0731) already used for the five topological-family "Seam D" codes in fieldnotes/2026-09-18-hackathon-1155-frontier-map-and-playbook.md. This pulls a different (p,q,N) entry from that same catalog, and is a sibling submission to 160-18-6.json and 660-68-8.json — both also {4,5} tessellations at different N.

Direction & hypothesis

Same direction as 80-18-5.note.md: filtering the source repo's own Hyperbolic_Codes.tsv index to N<=1000 gives 21 entries; only 5 (Seam D) were on the board. This is one of the 6 that checked out as still open.

What was searched

Same sweep as 80-18-5.note.md. Independently computed k matched the file's own header-comment [[n,k,d]] ([[360,38,8]] here).

Evidence trail

  • css.verify_css: CSS commutation confirmed.
  • css.compute_k: k=38, matching the file's own header.
  • submit.make_submission witness search (8,000 RIS trials/side, numpy,

    • seed 0): found a weight-8 witness on both sides, matching the paper's claimed distance.

  • Gate: verify/validate_candidate.py returned passed: true,

    • refute.refuted: false, novelty.board_advancing: true for (weight-6, unrestricted), dominated_by: [].

  • Claim: witness-backed upper bound, not exact.

Dead ends

See 80-18-5.note.md — same sweep, same 10 dominated entries not submitted.

Tools

Same as 80-18-5.note.md.

Reproduction

git clone https://github.com/QEC-pages/Quantum_LDPC_Codes.git
cd Quantum_LDPC_Codes
unzip Hyperbolic_Codes_Planar.zip -d hyp
# HX, HZ: hyp/4_5/4_5_360.mtx and hyp/4_5/5_4_360.mtx

import sys
sys.path.insert(0, "research/kit")
from submit import make_submission, save_submission
doc = make_submission(
    HX, HZ,
    name="[[360,38,8]] planar hyperbolic {4,5} code",
    construction="Planar hyperbolic {4,5} code, literature reproduction from "
                 "github.com/QEC-pages/Quantum_LDPC_Codes @ "
                 "1c95489383564e4dc2cce517de00d64d6f2c4f56, N=360.",
    authors=["@msilve160"], family="topological",
    references=["github.com/QEC-pages/Quantum_LDPC_Codes"],
    confidence="upper_bound", trials=8000, seed=0,
)
save_submission(doc, "codes/360-38-8.json")   # only after human review + PR

Parity checks

X-checks 144 (max weight 5) · Z-checks 180 (max weight 4)
H_X (144 checks, sparse supports)
[0, 2, 3, 7, 9] [0, 1, 5, 11, 13] [2, 4, 6, 14, 16] [1, 4, 10, 20, 22] [7, 15, 17, 29, 31] [3, 8, 18, 32, 34] [8, 11, 23, 39, 41] [5, 12, 24, 42, 44] [14, 21, 26, 46, 48] [6, 15, 27, 49, 51] [9, 19, 30, 35, 56] [12, 20, 36, 61, 63] [10, 21, 37, 64, 66] [13, 25, 40, 45, 71] [16, 28, 47, 52, 79] [29, 50, 53, 84, 86] [17, 30, 54, 87, 89] [19, 32, 57, 92, 94] [18, 33, 58, 95, 97] [22, 38, 62, 67, 103] [33, 39, 68, 108, 110] [23, 40, 69, 111, 113] [25, 42, 72, 116, 118] [24, 43, 73, 119, 121] [46, 65, 76, 124, 126] [26, 47, 77, 127, 129] [28, 49, 80, 132, 134] [27, 50, 81, 135, 137] [31, 55, 85, 90, 143] [56, 88, 91, 147, 149] [34, 59, 93, 98, 153] [35, 60, 99, 148, 159] [43, 61, 100, 160, 162] [36, 62, 101, 152, 163] [38, 64, 104, 167, 169] [37, 65, 105, 170, 172] [41, 70, 109, 114, 178] [71, 112, 115, 182, 184] [44, 74, 117, 122, 186] [45, 75, 123, 183, 192] [48, 78, 125, 130, 196] [79, 128, 131, 200, 202] [51, 82, 133, 138, 205] [52, 83, 139, 201, 210] [84, 136, 140, 211, 213] [53, 85, 141, 198, 214] [55, 87, 104, 168, 218] [54, 88, 144, 177, 219] [60, 92, 150, 224, 226] [57, 93, 102, 151, 163] [59, 95, 154, 230, 232] [58, 96, 155, 233, 235] [63, 102, 161, 165, 243] [103, 164, 166, 239, 246] [66, 106, 168, 173, 248] [67, 107, 174, 247, 253] [96, 108, 175, 254, 256] [68, 109, 145, 176, 219] [70, 80, 111, 133, 204] [69, 112, 179, 242, 260] [75, 116, 154, 231, 265] [72, 78, 117, 127, 185] [74, 119, 187, 267, 269] [73, 120, 188, 270, 272] [124, 171, 193, 276, 278] [76, 125, 194, 228, 279] [77, 128, 142, 197, 214] [83, 132, 203, 287, 289] [82, 135, 150, 225, 292] [81, 136, 206, 293, 295] [86, 142, 212, 216, 300] [143, 215, 217, 282, 303] [89, 145, 169, 221, 269] [90, 146, 193, 277, 304] [147, 174, 220, 252, 308] [91, 148, 222, 284, 309] [94, 152, 225, 228, 313] [153, 189, 227, 229, 270] [97, 156, 231, 236, 316] [98, 157, 237, 315, 317] [99, 158, 238, 246, 318] [120, 160, 240, 306, 320] [100, 161, 180, 241, 260] [101, 164, 195, 244, 279] [107, 167, 187, 268, 326] [106, 170, 203, 288, 327] [105, 171, 249, 328, 330] [110, 177, 255, 258, 334] [178, 217, 257, 259, 304] [113, 134, 180, 262, 288] [114, 140, 181, 212, 298] [139, 182, 209, 261, 297] [115, 183, 221, 263, 307] [118, 129, 198, 232, 284] [186, 237, 250, 266, 328] [121, 189, 268, 273, 342] [122, 190, 274, 317, 343] [123, 191, 200, 275, 283] [126, 195, 277, 281, 335] [196, 280, 282, 324, 332] [130, 199, 240, 303, 321] [131, 201, 285, 313, 346] [156, 205, 233, 290, 291] [137, 207, 226, 296, 352] [138, 208, 229, 315, 351] [211, 238, 249, 294, 329] [141, 215, 223, 301, 309] [146, 218, 305, 344, 353] [144, 220, 306, 336, 354] [149, 223, 253, 311, 355] [159, 239, 310, 319, 356] [158, 224, 312, 330, 341] [151, 227, 245, 314, 333] [157, 222, 230, 310, 331] [155, 234, 271, 308, 320] [162, 242, 301, 321, 323] [243, 259, 298, 322, 324] [165, 175, 245, 255, 332] [166, 247, 262, 325, 337] [207, 248, 274, 293, 305] [172, 250, 289, 331, 359] [173, 251, 291, 343, 351] [206, 234, 254, 275, 294] [176, 257, 264, 307, 335] [181, 204, 290, 299, 350] [179, 261, 278, 344, 357] [184, 210, 264, 339, 347] [192, 202, 286, 338, 348] [191, 265, 295, 340, 353] [185, 199, 266, 341, 354] [190, 263, 267, 296, 338] [188, 271, 276, 297, 329] [194, 280, 286, 334, 346] [197, 256, 283, 302, 333] [209, 272, 287, 314, 349] [208, 273, 285, 292, 347] [213, 244, 299, 318, 345] [241, 300, 319, 322, 337] [216, 302, 349, 356, 359] [311, 316, 323, 340, 357] [235, 252, 326, 350, 358] [236, 251, 325, 327, 355] [258, 312, 336, 348, 352] [281, 339, 342, 345, 358]
H_Z (180 checks, sparse supports)
[0, 1, 2, 4] [2, 6, 7, 15] [0, 3, 8, 11] [1, 5, 12, 20] [4, 10, 14, 21] [7, 9, 17, 30] [3, 9, 19, 32] [11, 13, 23, 40] [5, 13, 25, 42] [14, 16, 26, 47] [6, 16, 28, 49] [15, 27, 29, 50] [8, 18, 33, 39] [20, 22, 36, 62] [10, 22, 38, 64] [12, 24, 43, 61] [21, 37, 46, 65] [29, 31, 53, 85] [17, 31, 55, 87] [30, 54, 56, 88] [32, 34, 57, 93] [18, 34, 59, 95] [19, 35, 60, 92] [39, 41, 68, 109] [23, 41, 70, 111] [40, 69, 71, 112] [42, 44, 72, 117] [24, 44, 74, 119] [25, 45, 75, 116] [46, 48, 76, 125] [26, 48, 78, 127] [47, 77, 79, 128] [49, 51, 80, 133] [27, 51, 82, 135] [28, 52, 83, 132] [50, 81, 84, 136] [35, 56, 91, 148] [33, 58, 96, 108] [61, 63, 100, 161] [36, 63, 102, 163] [62, 101, 103, 164] [64, 66, 104, 168] [37, 66, 106, 170] [38, 67, 107, 167] [45, 71, 115, 183] [43, 73, 120, 160] [65, 105, 124, 171] [52, 79, 131, 201] [84, 86, 140, 212] [53, 86, 142, 214] [85, 141, 143, 215] [87, 89, 104, 169] [54, 89, 145, 219] [55, 90, 146, 218] [88, 144, 147, 220] [92, 94, 150, 225] [57, 94, 152, 163] [93, 151, 153, 227] [95, 97, 154, 231] [58, 97, 156, 233] [59, 98, 157, 230] [60, 99, 158, 224] [67, 103, 166, 247] [108, 110, 175, 255] [68, 110, 177, 219] [109, 176, 178, 257] [80, 111, 113, 134] [69, 113, 180, 260] [70, 114, 181, 204] [112, 179, 182, 261] [116, 118, 154, 232] [72, 118, 127, 129] [117, 185, 186, 266] [119, 121, 187, 268] [73, 121, 189, 270] [74, 122, 190, 267] [75, 123, 191, 265] [124, 126, 193, 277] [76, 126, 195, 279] [125, 194, 196, 280] [77, 129, 198, 214] [78, 130, 185, 199] [128, 197, 200, 283] [132, 134, 203, 288] [133, 204, 205, 290] [135, 137, 150, 226] [81, 137, 207, 293] [82, 138, 208, 292] [83, 139, 209, 287] [136, 206, 211, 294] [90, 143, 217, 304] [147, 149, 174, 253] [91, 149, 223, 309] [148, 159, 222, 310] [98, 153, 229, 315] [96, 155, 234, 254] [99, 159, 239, 246] [160, 162, 240, 321] [100, 162, 242, 260] [161, 241, 243, 322] [101, 152, 228, 279] [102, 151, 165, 245] [164, 244, 246, 318] [167, 169, 187, 269] [168, 218, 248, 305] [170, 172, 203, 289] [105, 172, 250, 328] [106, 173, 251, 327] [107, 174, 252, 326] [114, 178, 259, 298] [139, 182, 184, 210] [115, 184, 264, 307] [183, 192, 263, 338] [122, 186, 237, 317] [120, 188, 271, 320] [123, 192, 200, 202] [171, 249, 276, 329] [130, 196, 282, 303] [131, 202, 286, 346] [201, 210, 285, 347] [138, 205, 291, 351] [211, 213, 238, 318] [140, 181, 213, 299] [212, 298, 300, 322] [141, 198, 284, 309] [142, 197, 216, 302] [215, 301, 303, 321] [144, 177, 258, 336] [145, 176, 221, 307] [146, 193, 278, 344] [220, 306, 308, 320] [224, 226, 312, 352] [225, 285, 292, 313] [227, 270, 272, 314] [222, 230, 232, 284] [231, 265, 316, 340] [233, 235, 290, 350] [155, 235, 252, 308] [156, 236, 251, 291] [157, 237, 250, 331] [158, 238, 249, 330] [165, 243, 324, 332] [166, 239, 319, 337] [247, 253, 325, 355] [173, 248, 274, 343] [254, 256, 275, 283] [175, 245, 256, 333] [255, 280, 332, 334] [257, 277, 304, 335] [179, 242, 323, 357] [180, 241, 262, 337] [261, 276, 278, 297] [266, 328, 330, 341] [221, 263, 267, 269] [268, 326, 342, 358] [188, 209, 272, 297] [189, 208, 229, 273] [190, 207, 274, 296] [191, 206, 275, 295] [194, 228, 313, 346] [195, 244, 281, 345] [199, 240, 306, 354] [287, 289, 349, 359] [262, 288, 325, 327] [293, 295, 305, 353] [234, 271, 294, 329] [216, 300, 319, 356] [217, 259, 282, 324] [223, 301, 311, 323] [310, 331, 356, 359] [315, 317, 343, 351] [236, 311, 316, 355] [258, 286, 334, 348] [264, 281, 335, 339] [296, 338, 348, 352] [273, 339, 342, 347] [299, 345, 350, 358] [302, 314, 333, 349] [340, 344, 353, 357] [312, 336, 341, 354]
Code ID 360-38-8 · download JSON · raw on GitHub