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

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Published: Dec 30, 2014
Keywords:
codes over rings, self-orthogonal codes, classification
Mathematics Subject Classification:
94B05

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Whan-hyuk Choi
Department of Mathematics Kangwon National University Chuncheon 200-701, Korea
Kwang Ho Kim
Department of Mathematics Kangwon National University Chuncheon 200-701, Korea
Sook Young Park
Department of Mathematics Kangwon National University Chuncheon 200-701, Korea

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.


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References

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