Korean J. Math.  Vol 22, No 4 (2014)  pp.725-742
DOI: https://doi.org/10.11568/kjm.2014.22.4.725

The classification of self-orthogonal codes over $\mathbb Z_{p^2}$ of lengths $\leq$ 3

Whan-hyuk Choi, Kwang Ho Kim, Sook Young Park

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.

Keywords


codes over rings, self-orthogonal codes, classification

Subject classification

94B05

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References


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