Local search optimisation applied to the minimum distance problem

Abstract

In practical terms all coded electronic signals are prone to corruption during transmission but may be corrected by using error-correcting codes. The minimum distance of a code is important because it is the major parameter affecting the error-correcting performance of a code. In this paper a recent heuristic combinatorial optimisation algorithm, called ant colony optimisation (ACO), is applied to the problem of determining minimum distances of error-correcting codes. The ACO algorithm is motivated by analogy with natural phenomena, in particular, the ability of a colony of ants to ‘optimise’ their collective endeavours. In this paper the biological background for ACO is explained and its computational implementation is presented in an error-correcting code context. The particular implementation of ACO makes use of a tabu search (TS) improvement phase to give a computationally enhanced algorithm (ACOTS). Two classes of codes are then used to show that ACOTS is a useful and viable optimisation technique to investigate minimum distances of error-correcting codes.