Antoine Olivier

Listed in Henry Cohn’s table of spherical codes, each row credited Antoine Olivier, 2026.

Submitted 19 October 2026. Credit read in the table on 20 October 2026.

A spherical code is a set of N points on the unit sphere in dimension d; the goal is to keep the largest cosine between any two points as small as possible. For these ten (d, N) pairs, the new codes improve on the table values read on 19 October 2026, before submission.

New maximum cosine (certified upper bound, 12 decimals), table value before submission, and improvement (rounded; bar on a log scale from 10⁻¹⁰ to 10⁻⁴).

Local polishing by sequential linear programming. Eight codes start from entries the table marked as needing more optimization; (12, 92) and (13, 95) start from the codes with one more point by Ilmari Vahteristo and Luke Granto, minus one point.

Coordinates were scaled by 2⁵² and rounded to integers. Two independent programs (Python and PARI/GP) then checked in exact integer arithmetic that the largest cosine, which does not depend on scale, is at most the value shown. These are computational records, not proofs of optimality.

Computed in October 2026 with Claude Opus 5.5 (Anthropic) working as a coding agent in Claude Code under my direction. I take responsibility for the submission.

Listed in Andries Brouwer’s table of constant-weight codes, credit line Ol: Antoine Olivier, emails 2026-10-10, 2026-10-19, with 2+10 new codes.

Sent on 10 and 19 October 2026 and added by the maintainer. Ten of the twelve codes sent remain credited in the table on 20 October 2026.

A(n, d, w) is the largest number of binary words of length n and weight w with pairwise Hamming distance at least d. Each line below gives the new lower bound and the value the table listed when the code was sent.

• A(22, 6, 10) ≥ 2184 was 2183
• A(27, 6, 11) ≥ 19344 was 19305
• A(26, 8, 11) ≥ 2044 was 2042
• A(27, 8, 9) ≥ 1044 was 1029
• A(37, 8, 8) ≥ 2846 was 2845
• A(40, 8, 8) ≥ 3687 was 3683
• A(28, 10, 14) ≥ 817 was 814
• A(30, 10, 11) ≥ 514 was 512
• A(30, 10, 13) ≥ 940 was 936
• A(32, 10, 9) ≥ 307 was 305

Codes start from the table’s own code for the same cell and enlarge it. An integer linear program replaces a group of neighbouring words with a larger group; for A(27, 6, 11), 39 words could be added to the table’s code without removing any. Each file was checked by exact computation of length, weight, distinct words and minimum distance before sending.

This work was carried out with Claude Opus 5.5 (Anthropic) in Claude Code.

Credited in CONTRIBUTORS.md of the community project CrocSwap/integer-mult-bounds, for pull request #214.

Opened 9 October 2026; closed without merging on 14 October 2026, with the credit kept.

The project improves the exponent κ in an O(n (log n)^1−κ) bound for integer multiplication, within its stated conditional framework. I reran selected verification programs from four pull requests at recorded commits. Checks for #207 and #197 and a diagnostic for #199 reproduced. For #202, one check passed and another failed on a hash mismatch documented in the report. These runs do not validate the full theoretical framework. No new κ value.

I did this with help from Claude (Anthropic) agents; the runs were done locally.