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

Lucky Erap Galvez, Rowena Alma Betty, Fidel Nemenzo

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.

Keywords

codes over rings; self-orthogonal codes; mass formula

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