Self-orthogonal Codes over Fq + uFq and Fq + uFq + u 2Fq

Authors

  • Lucky Erap Galvez Institute of Mathematics University of the Philippines Diliman https://orcid.org/0000-0003-4888-0425
  • Rowena Alma Betty Institute of Mathematics University of the Philippines Diliman
  • Fidel Nemenzo Institute of Mathematics University of the Philippines Diliman

DOI:

https://doi.org/10.29020/nybg.ejpam.v13i4.3838

Keywords:

codes over rings, self-orthogonal codes, mass formula

Abstract

In this paper, we establish a mass formula for Euclidean and Hermitian self-orthogonal codes over the finite ring Fq + uFq, where Fq is the finite field of order q and u2 = 0. We also establish a mass formula for Euclidean self-orthogonal codes over the finite ring Fq + uFq + u2Fq, with u3 = 0 and characteristic of Fq is odd. These mass formulas are used to give a classification of Euclidean and Hermitian self-orthogonal codes over F2 + uF2 and F3 + uF3 of small lengths.

Author Biography

  • Lucky Erap Galvez, Institute of Mathematics University of the Philippines Diliman
    Assistant Professor

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Published

2020-10-31

Issue

Vol. 13 No. 4: (October 2020)

Section

Nonlinear Analysis

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Self-orthogonal Codes over Fq + uFq and Fq + uFq + u 2Fq. (2020). European Journal of Pure and Applied Mathematics, 13(4), 873-892. https://doi.org/10.29020/nybg.ejpam.v13i4.3838

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