Four New Single-Error-Correcting Binary Codes

Moshe Milshtein

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arXiv · 2610.23626

Four New Single-Error-Correcting Binary Codes

Moshe Milshtein

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Abstract

We construct a $(16, 3072, 3)$-code, a $(17,6144,3)$-code, an $(18,12288,3)$-code and a $(19,24576,3)$-code. Consequently, we get four new lower bounds: $A(16,3) \geq 3072$, $A(17,3) \geq 6144$, $A(18,3) \geq 12288$ and $A(19,3) \geq~24576$. Each of the codes consists of a union of cosets of a linear code. The constructions are the result of a computer search executing a tabu search algorithm.

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Moshe Milshtein. 2026-10-16. Four New Single-Error-Correcting Binary Codes. https://arxiv.org/abs/2610.23626

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