On the Computing of the Minimum Distance of Linear Block Codes by Heuristic Methods

TL;DR

This paper introduces two heuristic methods, genetic algorithms and a novel randomized approach called Multiple Impulse Method, to estimate the minimum distance of linear block codes, a problem difficult for classical techniques.

Contribution

It presents a new randomized algorithm, MIM, and compares its effectiveness with existing genetic algorithm approaches for computing minimum distances.

Findings

Genetic algorithms yield good results in minimum distance estimation.

The MIM algorithm effectively finds low-weight codewords.

The methods outperform classical techniques in certain cases.

Abstract

The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call Multiple Impulse Method MIM, where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.