Optimal, Divisible binary Codes from Gray-Homogeneous Images of Codes over R_{k,m}
Keywords:
Homogeneous Weight, Frobenius rings, divisible codes, self-orthogonal quasicyclic codes, optimal codesAbstract
In this work, we find a form for the homogeneous weight over the ring R_{k,m}, using the related theoretical results from the literature. We then use the first order Reed-Muller codes to find a distance-preserving map that takes codes over R_{k,m} to binary codes. By considering cyclic, constacyclic and quasicyclic codes over R_{k,m} of different lengths for different values of k and m, we construct a considerable number of optimal binary codes that are divisible with high levels of divisibility. The codes we have obtained are also quasicyclic with high indices and they are all self-orthogonal when km\geq 4 The results, which have been obtained by computer search are tabulated.Downloads
Published
2017-11-02
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Section
Coding Theory and Cryptology
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How to Cite
Optimal, Divisible binary Codes from Gray-Homogeneous Images of Codes over R_{k,m}. (2017). European Journal of Pure and Applied Mathematics, 10(5), 1112-1123. https://www.ejpam.com/index.php/ejpam/article/view/2650