The Mass Formula for Symplectic Self-Orthogonal Codes Over a Non-unitary Ring of Order 9

Abstract

Duality of codes over a commutative non-unitary ring of order 9 using the symplectic inner product is explored. For codes over this ring, there are two associated ternary codes, called residue code and torsion code. By studying the residue and torsion codes, conditions for symplectic orthogonality will be explored and a mass formula for symplectic self-orthogonal codes will be derived.