Quasi-Self-Dual Codes over a Non-Unital Ring of Order 4

Abstract

We relate quasi-self-dual codes over a non-unital ring to additive self-dual codes over the additive group of the ring. We show that the Hamming weight enumerator of a quasi-self-dual code over this non-unital ring must belong to the same ring of invariants that self-dual codes over the Frobenius rings with unities belong. Additionally, the Hamming weight enumerator of a Type IV code over E E must reside in the same ring of invariants as a Type IV code over the field of order 4 4 .