An Application of the Virus Optimization Algorithm to the Problem of Finding Extremal Binary Self-Dual Codes

Adrian Korban, Serap Sahinkaya, Deniz Ustun

In this paper, a virus optimization algorithm, which is one of the metaheuristic optimization technique, is employed for the first time to the problem of finding extremal binary self-dual codes. We present a number of generator matrices of the form $[I_{36} \ | \ \tau_3(v)],$ where $I_{36}$ is the $36 \times 36$ identity matrix, $v$ is an element in the group matrix ring $M_3(\mathbb{F}_2)G$ and $G$ is a finite group of order 12, which we then employ together with the the virus optimization algorithm and the genetic algorithm to search for extremal binary self-dual codes of length 72. We obtain that the virus optimization algorithm finds more extremal binary self-dual codes than the genetic algorithm. Moreover, by employing the above mentioned constructions together with the virus optimization algorithm, we are able to obtain 39 Type I and 19 Type II codes of length 72, with parameters in their weight enumerators that were not known in the literature before.

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