Convolutional codes with a maximum distance profile based on skew polynomials

TL;DR

This paper introduces a new family of convolutional codes with maximum distance profiles, utilizing skew polynomial theory to improve field size efficiency over previous methods.

Contribution

It presents a novel construction of convolutional codes with maximum distance profiles based on skew polynomials, reducing the required field size.

Findings

Constructed (n,k) convolutional codes with degree  in {k,n-k}

Achieved smaller field size of order n^{2}

Improved upon existing maximum distance profile code constructions

Abstract

We construct a family of (n,k) convolutional codes with degree \delta in {k,n-k} that have a maximum distance profile. The field size required for our construction is of the order n^{2\delta}, which improves upon the known constructions of convolutional codes with a maximum distance profile. Our construction is based on the theory of skew polynomials.