Discovery of good double and triple circulant codes using multiple impulse method

Abstract: The construction of optimal linear block error-correcting codes is not an easy problem, for this, many studies describe methods for generating good error correcting codes in terms of minimum distance. In a previous work, we have presented the multiple impulse method (MIM) to evaluate the minimum distance of linear codes. In this paper we will present an optimization of the MIM method by genetic algorithms, and we found many new optimal Double and Triple Circulant Codes (DCC & TCC) with the highest known parameters using the MIM method as an evaluator of the minimum distance. Two approaches are used in the exploration of the space of generators; the first is based on genetic algorithms, however the second is on the random search algorithm.