On the Error-correcting Capability of Twisted Centralizer Codes Obtained from a Fixed Rank-1 Matrix

TL;DR

This paper generalizes the error-correcting capabilities of twisted centralizer codes derived from a fixed rank-1 matrix, revealing they are maximum distance separable despite low information rate.

Contribution

It introduces a generalization of twisted centralizer codes based on a fixed rank-1 matrix, analyzing their properties and error-correcting potential.

Findings

Codes have dimension 1 for any fixed combinatorial matrix

Codes are maximum distance separable

Low information rate due to code construction

Abstract

In this paper, we give a generalization on the error correcting capability of twisted centralizer codes obtained from a fixed rank 1 matrix. In particular, we fix the combinatorial matrix which is obtained by getting the linear combination of the matrix whose all entries are 1 and the identity matrix of order n. Results reveal that such codes have a dimension 1 for any fixed combinatorial matrix and constant a hence having a relatively low information rate due to the way its codewords are constructed, but are found to be maximum distance separable codes.