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Small classical codes: extended ternary Golay, [16,5,8] RM, [15,4,8] simplex, [4,3,2] SPC - #402
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…[15,4,8] simplex, [4,3,2] SPC New entries, built mostly from text moved out of other entries: - extended_ternary_golay ([12,6,6]_3): description, decoder, and the extended-code cousins move out of ternary_golay; pless_symmetry (q=5), divisible, and delsarte_optimal_q-ary become parents; niemeier, tetracode, and the S(5,6,12) half of combinatorial_design are retargeted. - rm_16_5_8 ([16,5,8] first-order RM): the biorthogonal cousins of extended_golay, lambda16, nordstrom_robinson, and stab_16_6_4 are retargeted; bch~griesmer becomes a griesmer parent. - simplex_15_4_8 ([15,4,8] simplex): stab_15_4_3 and stab_15_6_3 simplex cousins retargeted; bch parent (designed distance eight). - spc_4_3_2 ([4,3,2] SPC): classical counterpart of the [[4,2,2]] and [[4,1,2]] LNCY codes; parity_check~stab_4_2_2 and dfour~parity_check retargeted; small_distance is inherited through parity_check (rule 15). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
…nts, verified citations
- simplex: bch parent (b=0, designed distance 2^{m-1}, MacSlo Ch. 7 Prob. 23)
replaces binary_cyclic, now implied; the shift-register fact moves into the
description. simplex_15_4_8 drops its bch edge and the [15,5,7] sentence,
and its opener names the [[15,7,3]] quantum Hamming code, which gains a
cousin. stab_15_6_3/stab_15_4_3 quantum_bch details say b=0 and are split.
- extended_ternary_golay: projective becomes a parent; divisible moves to
pless_symmetry (MacSlo Ch. 16 Thm. 17); Pless q=5 detail cites MacSlo
Ch. 16 Prob. 18; sharp-configuration detail tightened.
- biorthogonal: griesmer and projective parents; rm_16_5_8 drops griesmer and
keeps the BCH extension as a description sentence (MacSlo Ch. 13 Thm. 11).
- spc_4_3_2: stabilizer wording; RM(1,2) detail cites MacSlo Ch. 13 Prob. 5.
- griesmer: drop stale comment.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
…tations - biorthogonal projective detail states the m>=2 range for the duality reason. - simplex_15_4_8 opener split into two sentences. - simplex bch detail cites MacSlo Ch. 7 Thm. 8 (BCH bound, general b) with Prob. 23. - extended_ternary_golay projective detail cites MacSlo Ch. 16 Thm. 17 and Prob. 18. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Resolve extended_golay: keep the restored orthogonal_array and self_dual cousins from fix/classical-cleanup and the rm_16_5_8 retarget from this branch. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
valbert4
commented
Oct 14, 2026
Drop the quantum stabilizer sentence from the [4,3,2] SPC description; the cousins to stab_4_2_2 and css_4_1_2 keep the link. Move the extended-BCH construction of the [16,5,8] RM code into a bch cousin. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
nordstrom_robinson: MacSlo pg. 74 (not 76) states NR = [16,5,8] RM plus 7 cosets. lambda16: SPLAG Construction B sentence is on pg. 129, figure on pg. 130. extended_ternary_golay: MacSlo pg. 178 gives both self-duality and distance 6. simplex: MacSlo pg. 221 states that theta_1 generates the simplex code; the BCH zeros hold for a suitable primitive element. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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Stacked on #401 (base fix/classical-cleanup); retarget to main once #401 merges.
New extended_ternary_golay: [12,6,6]_3 extended ternary Golay code (text moved from ternary_golay; parents pless_symmetry, delsarte_optimal_q-ary, projective)
New rm_16_5_8: [16,5,8] first-order RM code (biorthogonal cousins of extended_golay, lambda16, nordstrom_robinson, stab_16_6_4 retargeted to it)
New simplex_15_4_8: [15,4,8] simplex code (simplex cousins of stab_15_4_3, stab_15_6_3 retargeted; new cousin stab_15_7_3)
New spc_4_3_2: [4,3,2] single-parity-check code, classical counterpart of the [[4,1,2]] and [[4,2,2]] codes
Edited ternary_golay, pless_symmetry, niemeier, tetracode, combinatorial_design, delsarte_optimal_q-ary: text and relations moved to extended_ternary_golay
Edited simplex: new bch parent (b=0, designed distance 2^{m-1}), replacing binary_cyclic
Edited biorthogonal: new griesmer and projective parents
Edited pless_symmetry: new divisible parent
Edited parity_check, dfour, stab_4_2_2, css_4_1_2, stab_15_4_3, stab_15_6_3, stab_15_7_3, bch, griesmer: relations retargeted to the new specific entries
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