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

Main Article Content

Whan-hyuk Choi
Kwang Ho Kim
Sook Young Park


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.

Article Details


[1] R.A.L. Betty and A. Munemasa, Mass formula for self-orthogonal codes over Zp2 , Journal of combinatorics, information & system sciences 34 (2009), 51–66. Google Scholar

[2] W. Cary Huffman and Vera Pless, Fundamentals of error correcting codes, Cambridge University Pless, New York, 2003. Google Scholar

[3] W. Choi and Y.H. Park, Self-dual codes over Zp2 of length 4, preprint. Google Scholar

[4] J.H. Conway and N.J.A. Sloane, Self-dual codes over the integers modulo 4, J. Comin. Theory Ser. A. 62 (1993), 30–45. Google Scholar

[5] S.T. Dougherty, T.A. Gulliver, Y.H. Park, J.N.C. Wong, Optimal linear codes oner Zm, J. Korean. Math. Soc. 44 (2007), 1136–1162. Google Scholar

[6] Y. Lee and J. Kim, An efficient construction of self-dual codes, CoRR, 2012. Google Scholar

[7] K. Nagata, F. Nemenzo and H. Wada, Constructive algorithm of self-dual error-correcting codes, 11th International Workshop on Algebraic and Combinatorial Coding Theory, 215–220, 2008. Google Scholar

[8] Y.H. Park, The classification of self-dual modular codes, Finite Fields and Their Applications 17 (5) (2011), 442–460. Google Scholar

[9] V.S. Pless, The number of isotropic subspace in a finite geometry, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei 39 (1965), 418–421. Google Scholar

[10] V.S. Pless, On the uniqueness of the Golay codes, J. Combin. Theory 5 (1968), 215–228. Google Scholar