Approaching the Minimum Distance Problem by Algebraic Swarm-Based Optimizations

Abstract

Finding the minimum distance of linear codes is one of the main problems in coding theory. The importance of the minimum distance comes from its error-correcting and error-detecting capability of the handled codes. It was proven that this problem is an NP-hard that is the solution of this problem can be guessed and verified in polynomial time but no particular rule is followed to make the guess and some meta-heuristic approaches in the literature have been used to solve this problem. In this paper, swarm-based optimization techniques, bat and firefly, are applied to the minimum distance problem by integrating the algebraic operator to the handled algorithms.