Shenoy, Ajitha K B and Biswas, Somenath and Kurur, Piyush P (2014) Performance of Metropolis Algorithm for the Minimum Weight Code Word Problem. In: GECCO’14, July 12–16, 2014, Vancouver, BC, Canada.

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Abstract

We study the performance of the Metropolis algorithm for the problem of finding a code word of weight less than or equal to M, given a generator matrix of an [n; k]-binary linear code. The algorithm uses the set Sk of all k x k in- vertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other via an elementary row operation (i.e by adding one row to an- other or by swapping two rows.) We prove that the Markov chains associated with the Metropolis algorithm mix rapidly for suitable choices of the temperature parameter T. We ran the Metropolis algorithm for a number of codes and found that the algorithm performed very well in comparison to previously known experimental results.

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