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

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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