Mutation-Based Algebraic Artificial Bee Colony Algorithm for Computing the Distance of Linear Codes

Abstract

Finding the minimum distance of linear codes is a non-deterministic polynomial-time-hard problem and different approaches are used in the literature to solve this problem. Although, some of the methods focus on finding the true distances by using exact algorithms, some of them focus on optimization algorithms to find the lower or upper bounds of the distance. In this study, we focus on the latter approach. We first give the swarm intelligence background of artificial bee colony algorithm, we explain the algebraic approach of such algorithm and call it the algebraic artificial bee colony algorithm (A-ABC). Moreover, we develop the A-ABC algorithm by integrating it with the algebraic differential mutation operator. We call the developed algorithm the mutation-based algebraic artificial bee colony algorithm (MBA-ABC). We apply both; the A-ABC and MBA-ABC algorithms to the problem of finding the minimum distance of linear codes. The achieved results indicate that the MBA-ABC algorithm has a superior performance when compared with the A-ABC algorithm when finding the minimum distance of Bose, Chaudhuri, and Hocquenghem (BCH) codes (a special type of linear codes).

Keywords

• Minimum distance
• minimum-weight codeword
• optimisation
• heuristic
• artificial bee colony algorithm

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