Self-dual codes over ${\mathbb Z}_{p^2}$ of small lengths

Abstract

Self-dual codes of lengths less than 5 over ${\mathbb Z}_p$ are completely classified by the second author [The classification of self-dual modular codes, Finite Fields Appl. 17 (2011), 442-460].The number of such self-dual codes are also determined. In this article we will extend the results to classify self-dual codes over ${\mathbb Z}_{p^2}$ of length less than 5 and give the number of codes in each class. Explicit and complete classifications for small $p$'s are also given.