Mass Formula for Self-Dual Codes over Galois Rings GR(p3, r)

Trilbe Lizann Espina Vasquez, Gaudencio Jr. Cempron Petalcorin

Abstract

Let p be an odd prime and r a positive integer. Let GR(p3, r) be the Galois ring of characteristic p3 and cardinality p3r. In this paper, we investigate the self-dual codes over GR(p3, r) and give a method to construct self-dual codes over this ring. We establish a mass formula for self-dual codes over GR(p3, r) and classify self-dual codes over GR(p3, 2) of length 4 for p = 3, 5.

Keywords

mass formula; self-dual codes; finite ring; Galois ring; classification

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