Optimal, Divisible binary Codes from Gray-Homogeneous Images of Codes over R_{k,m}

Authors

  • Bahattin Yildiz Northern Arizona University
  • Nesibe Tufekci

Keywords:

Homogeneous Weight, Frobenius rings, divisible codes, self-orthogonal quasicyclic codes, optimal codes

Abstract

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.

Author Biography

  • Bahattin Yildiz, Northern Arizona University
    Mathematics & Statistics, Assistant Professor

Downloads

Published

2017-11-02

Issue

Vol. 10 No. 5: (October 2017)

Section

Coding Theory and Cryptology

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

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