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arXiv · 1709.02195

Uniqueness of codes using semidefinite programming

Andries E. Brouwer·Sven C. Polak
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Abstract

For $n,d,w \in \mathbb{N}$, let $A(n,d,w)$ denote the maximum size of a binary code of word length $n$, minimum distance $d$ and constant weight $w$. Schrijver recently showed using semidefinite programming that $A(23,8,11)=1288$, and the second author that $A(22,8,11)=672$ and $A(22,8,10)=616$. Here we show uniqueness of the codes achieving these bounds. Let $A(n,d)$ denote the maximum size of a binary code of word length $n$ and minimum distance $d$. Gijswijt, Mittelmann and Schrijver showed that $A(20,8)=256$. We show that there are several nonisomorphic codes achieving this bound, and classify all such codes with all distances divisible by 4.

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BibTeXRIS

Andries E. Brouwer, Sven C. Polak. 2017-09-07. Uniqueness of codes using semidefinite programming. https://doi.org/10.1007/s10623-018-0589-8

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