New Linear Codes from Matrix-Product Codes with Polynomial Units
Fernando Hernando, Diego Ruano
TL;DR
The paper addresses improving linear code parameters by extending matrix-product constructions with polynomial units over polynomial rings. It analyzes a distance bound for these codes, and develops a Plotkin-type construction using polynomial units and nested cyclic codes to surpass the bound in practice. The authors produce several new binary codes with improved parameters and a wide range of quasi-cyclic codes that reach best-known bounds, demonstrating the practical potential of polynomial-unit matrix-product codes. This work broadens the coding-construction toolkit for high-distance quasi-cyclic codes and highlights the utility of polynomial-unit structures for code design.
Abstract
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.