抄録
Self-dual codes have been widely studied in cod-ing theory, both over nite elds and over rings. Af-ter the discovery that several well-known families of non-linear binary codes are intimately related to lin-ear codes over the ring Z4 (the ring of integers mod-ulo 4), much attention have been given to codes over rings, speci cally rings with unity. Only recently re-searchers begun to explore non-unital rings as alpha-bet [1, 2] The absence of a multiplicative identity cre-ates difficulties in dealing with the usual concept of self-duality in a code. As a result, the notion of quasi self-dual (QSD) codes was introduced [1], that is, self-orthogonal codes of size pⁿ.
The goal of this paper is to present some basic theory on the duality of codes over a non-local, non-unital ring Hp in the classi cation of Fine [3]. We characterize self-orthogonal, self-dual and quasi self-dual codes over Hp.
