On decoding procedures of intertwining codes

TL;DR

This paper introduces intertwining codes with variable length, proposes two decoding methods applicable to these and other linear codes, and demonstrates how linear codes can be embedded into intertwining codes.

Contribution

It presents a new class of matrix equation codes called intertwining codes with flexible length and offers two decoding algorithms suitable for these and other linear codes.

Findings

Intertwining codes have length of the form nk.

Two decoding methods are established for intertwining codes.

Linear codes can be embedded into intertwining codes.

Abstract

One of the main weakness of the family of centralizer codes is that its length is always $n^2$. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form $nk$. We establish two decoding methods which can be fitted to intertwining codes as well as for any linear codes. We also show an inclusion of linear codes into a special class of intertwining codes.