On interpolation-based decoding of a class of maximum rank distance codes

TL;DR

This paper introduces an efficient interpolation-based decoding algorithm for a recently proposed family of maximum rank distance codes, leveraging properties of Dickson matrices and a modified Berlekamp-Massey algorithm to achieve polynomial-time decoding.

Contribution

It presents a novel decoding method for maximum rank distance codes using interpolation and matrix properties, improving decoding efficiency within the unique decoding radius.

Findings

Decoding reduces to solving a quadratic polynomial when errors are within the unique radius.

The algorithm operates in polynomial time.

It effectively decodes a specific class of maximum rank distance codes.

Abstract

In this paper we present an interpolation-based decoding algorithm to decode a family of maximum rank distance codes proposed recently by Trombetti and Zhou. We employ the properties of the Dickson matrix associated with a linearized polynomial with a given rank and the modified Berlekamp-Massey algorithm in decoding. When the rank of the error vector attains the unique decoding radius, the problem is converted to solving a quadratic polynomial, which ensures that the proposed decoding algorithm has polynomial-time complexity.