Twisted Permutation Codes

TL;DR

This paper introduces twisted permutation codes, a new class of frequency permutation arrays, demonstrating they can have minimum distances exceeding traditional bounds, thus offering improved error-correcting capabilities.

Contribution

The paper defines twisted permutation codes, establishes a lower bound for their minimum distance, and provides examples where this bound is tight or exceeded, advancing permutation code theory.

Findings

Lower bound for minimum distance established

Examples where the bound is tight

Examples with minimum distance greater than the bound

Abstract

We introduce twisted permutation codes, which are frequency permutation arrays analogous to repetition permutation codes, namely, codes obtained from the repetition construction applied to a permutation code. In particular, we show that a lower bound for the minimum distance of a twisted permutation code is the minimum distance of a repetition permutation code. We give examples where this bound is tight, but more importantly, we give examples of twisted permutation codes with minimum distance strictly greater than this lower bound.