combinatorics / Coding theory; algebraic graph theory; discrete geometry

Optimality of the added-vector code in the 19-dimensional kissing construction

For the fixed five-punctured extended binary Golay ambient code DD used in the 19-dimensional added-vector kissing construction, determine the largest subset with minimum Hamming distance at least 55, without a linearity assumption.

48Significance / 100
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Acceptance criteria: Keep the fixed-code optimum separate from the unrestricted kissing number k(19)k(19), and preserve the source's explicit computer-assisted and review boundaries.

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combinatoricsSep 6, 2026Significance 48/100

Fixed 19-dimensional added-vector code optimum reported

Prior state unknownFixed added-vector code optimum α5(D)=1280\alpha_5(D)=1280 source-authenticated; unrestricted k(19)k(19) remains open

VibeMathed recorded: Fixed 19-dimensional added-vector code optimum reported. Consult the linked registry entry for the original report and scope.

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Source authenticated

For the fixed ambient binary code DD in the manuscript, every subset AA with minimum Hamming distance at least 55 has size at most 1280, and Ho's construction attains 1280; equivalently α5(D)=1280\alpha_5(D)=1280. The same certificate gives α5(K)=320\alpha_5(K)=320 for the stated 1024-word subcode KK. This does not bound the unrestricted kissing number k(19)k(19).

The source's explicit code coordinates, five-word Clebsch-graph certificate, coset argument, and exact verifier are accepted only as source-authenticated evidence in this draft; MFN did not execute the verifier.

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