Encoding and Decoding of Several Optimal Rank Metric Codes

TL;DR

This paper develops efficient encoding and decoding algorithms for various optimal rank metric codes based on symmetric, alternating, and Hermitian matrices, enabling reliable error correction in polynomial time.

Contribution

It introduces evaluation encoding and reversible methods, along with interpolation-based decoding algorithms for these specialized rank metric codes, enhancing their practical applicability.

Findings

Decoding algorithms can correct errors up to half the minimum distance.

Encoding methods are reversible and suitable for these codes.

Algorithms operate in polynomial time.

Abstract

This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right choice for these codes and then we provide easily reversible encoding methods for each family. Later unique decoding algorithms for the codes are described. The decoding algorithms are interpolation-based and can uniquely correct errors for each code with rank up to $\lfloor(d-1)/2\rfloor$ in polynomial-time, where $d$ is the minimum distance of the code.