THE CLASSIFICATION OF SELF-ORTHOGONAL CODES OVER ℤp2OF LENGTHS ≤ 3

Abstract

In this paper, we find all inequivalent classes of self-orthogonal codes over $\mathbb Z_{p^2}$ of lengths $l \leq 3$ for all primes $p$, using similar method as in [3]. We find that the classification of self-orthogonal codes over $\mathbb Z_{p^2}$ includes the classification of all codes over $\mathbb Z_{p}$. Consequently, we classify all the codes over $\mathbb Z_{p}$ and self-orthogonal codes over $\mathbb Z_{p^2}$ of lengths $l \leq3$ according to the automorphism group of each code.