Published October 29, 2026 | Version v1

Strictly self-dual CSS codes whose permutation logical groups are the full Sp(6,F2), O(6,F2), O(7,F2) and O(8,F2)

Authors/Creators

  • 1. Independent researcher

Description

In a strictly self-dual CSS code, both stabilizer spaces are one binary code C. The qubit permutations that preserve the code induce on the logical space a subgroup of Sp(k,F2) if the all-ones vector lies in C, and a subgroup of O(k,F2) otherwise. Koh, Majidy, Chakraborty, Gong, Tan and Yao (arXiv:2609.19250) gave codes that reach the full group for k ≤ 4 and k ≤ 5 respectively, proved that it cannot be reached for k ≥ 8 and k ≥ 9, and asked about the cases in between. We answer all four open cases in the affirmative with explicit indecomposable strictly self-dual codes: [[318,6]] with Sp(6,F2), [[319,7]] with O(7,F2), [[246,6]] with O(6,F2) and [[4350,8]] with O(8,F2). With their results, this decides for every k whether these bounds are attained. The codes come from permutation modules in which a Witt reduction leaves exactly the natural module of the target group in C⊥/C. Two programs written in separate AI agent sessions check every code, and a third checks the three smaller ones. The distances satisfy 8 ≤ d ≤ 16 with d even, 7 ≤ d ≤ 15, 7 ≤ d ≤ 10 and 7 ≤ d ≤ 438. This record holds the paper, its LaTeX source, and a zip with the codes, scripts and logs.

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References
arXiv:2609.19250 (arXiv)