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Add self-orthogonal CSS(RM(r,m),RM(r,m)) family and its distance to quantum_reed_muller entry - #384

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sdoygb wants to merge 3 commits into
errorcorrectionzoo:mainfrom
sdoygb:zoo-qrm-update
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sdoygb wants to merge 3 commits into
errorcorrectionzoo:mainfrom
sdoygb:zoo-qrm-update

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@sdoygb

@sdoygb sdoygb commented Sep 14, 2026

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Re-submitted. This supersedes #381, which GitHub permanently closed when its source fork was deleted — a pull request cannot be reopened once its head repository is gone.
Branch and commit are identical to the original.

This PR adds to the quantum Reed-Muller entry:

  1. The CSS(RM(r,m), RM(r,m)) family (self-orthogonal for 2r < m-1), with explicit parameters [[2^m, 2^m - 2*Sum_{j<=r} C(m,j), 2^(r+1)]] and the distance derivation from the RM minimum-weight theorem (MacWilliams-Sloane, Ch. 13).
  2. A distance feature noting that the distance of this family admits a certificate checkable without enumerating the exponentially many error patterns: for r >= 1, column-distinctness of the RM check matrix (no weight-2 logicals), the RM minimum-weight theorem (no intermediate weights), and affine (r+1)-flat indicators as weight-2^(r+1) vectors in RM(m-r-1,m) \ RM(r,m) saturating the bound.

Checklist

Verification note

Family parameters and the certificate were verified numerically for members
[[32,20,4]], [[64,50,4]], [[64,20,8]], [[128,70,8]], [[256,70,16]], [[512,252,16]], [[1024,252,32]]:
weight-4 layer counts (1240 and 10416) match the affine-flat counting formula exactly, and
[[64,20,8]] passed a full brute-force check of all 7.05e8 error sets of weight 1..7 with zero undetected.

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