Increasing the minimum distance of codes by twisting

TL;DR

This paper introduces new infinite families of twisted permutation codes that have higher minimum distances than their corresponding repetition permutation codes, enhancing error-correcting capabilities.

Contribution

The authors construct two new infinite families of twisted permutation codes with strictly greater minimum distances than traditional repetition permutation codes.

Findings

Two new infinite families of codes with improved minimum distances

Twisted permutation codes can outperform repetition permutation codes in error correction

Minimum distance can be strictly larger in twisted codes

Abstract

Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller code. It was previously shown that the minimum distance of a twisted permutation code is at least the minimum distance of a corresponding repetition permutation code, but in some instances can be larger. We construct two new infinite families of twisted permutation codes with minimum distances strictly greater than those for the corresponding repetition permutation codes.