Combining ILS with an effective constructive heuristic for the application to error correcting code design

Error correcting code (ECC) design is a hard optimization problem arising in telecommunication applications. In the electronic transmission of messages it often happens—due to noisy channels—that the arriving message is corrupted. One solution to this problem consists in transmitting the message several times in order to increase the probability of its safe arrival. However, this is often too costly. Instead, it is nowadays standard to use ECC. In this paper we focus on the design of linear block codes. In particular, we want to find the best possible code for a given number of code-words M with a given length n, i.e., a code where the minimum Hamming distance d between code-words is as big as possible. For this purpose we propose an iterated local search algorithm that uses a particular constructive heuristic for generating the initial solution. The experimental results show that our algorithm is currently a state-of-the-art method for the ECC problem.