Minimum distance computation of linear codes via genetic algorithms with permutation encoding

TL;DR

This paper introduces a genetic algorithm with permutation encoding to efficiently estimate the upper bound of the minimum distance of linear codes, independent of the field size or code dimension.

Contribution

It presents a novel permutation encoding approach for genetic algorithms to compute bounds on linear code minimum distances, improving scalability.

Findings

Method's efficiency grows non-polynomially with code length

Permutation encoding reduces problem complexity

Effective heuristic for large linear codes

Abstract

We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the problem, so that its space of solutions does not depend on the size of the base field or the dimension of the code. Actually, the efficiency of our method only grows non-polynomially with respect to the length of the code.