Linear MSRD codes with Various Matrix Sizes and Unrestricted Lengths

TL;DR

This paper introduces a new construction method for linear maximum sum-rank distance (MSRD) codes over arbitrary fields, accommodating various matrix sizes and unrestricted lengths, thus broadening the applicability of such codes.

Contribution

The paper presents a novel construction of linear MSRD codes for arbitrary matrix sizes and lengths, satisfying specific size conditions, extending previous limited parameter cases.

Findings

Constructed MSRD codes for various matrix sizes

Codes achieve the Singleton bound in sum-rank metric

Applicable over any finite field ${f F}_q$

Abstract

A sum-rank-metric code attaining the Singleton bound is called maximum sum-rank distance (MSRD). MSRD codes have been constructed for some parameter cases. In this paper we construct a linear MSRD code over an arbitrary field ${\bf F}_q$ with various matrix sizes $n_1>n_2>\cdots>n_t$ satisfying $n_i \geq n_{i+1}^2+\cdots+n_t^2$ for $i=1, 2, \ldots, t-1$ for any given minimum sum-rank distance.