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)

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23762200
Primary Topic
Coding theory and cryptography
Type
preprint
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preprint

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)

Maximilian Kornstein
Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
preprint

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)

Maximilian Kornstein
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
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