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http://dx.doi.org/10.11568/kjm.2014.22.4.725

THE CLASSIFICATION OF SELF-ORTHOGONAL CODES OVER ℤp2 OF LENGTHS ≤ 3  

Choi, Whan-Hyuk (Department of Mathematics Kangwon National University)
Kim, Kwang Ho (Department of Mathematics Kangwon National University)
Park, Sook Young (Department of Mathematics Kangwon National University)
Publication Information
Korean Journal of Mathematics / v.22, no.4, 2014 , pp. 725-742 More about this Journal
Abstract
In this paper, we find all inequivalent classes of self-orthogonal codes over $Z_{p^2}$ 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 $Z_{p^2}$ includes the classification of all codes over $Z_p$. Consequently, we classify all the codes over $Z_p$ and self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ according to the automorphism group of each code.
Keywords
codes over rings; self-orthogonal codes; classification;
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1 R.A.L. Betty and A. Munemasa, Mass formula for self-orthogonal codes over $\mathbb{Z}_{p2}$, Journal of combinatorics, information & system sciences 34 (2009), 51-66.
2 W. Cary Hu man and Vera Pless, Fundamentals of error correcting codes, Cambridge University Pless, New York, 2003.
3 W. Choi and Y.H. Park, Self-dual codes over $\mathbb{Z}_{p2}$ of length 4, preprint.
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.   DOI
5 S.T. Dougherty, T.A. Gulliver, Y.H. Park, J.N.C. Wong, Optimal linear codes oner $\mathbb{Z}_m$, J. Korean. Math. Soc. 44 (2007), 1136-1162.
6 Y. Lee and J. Kim, An efficient construction of self-dual codes, CoRR, 2012.
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.
8 Y.H. Park, The classification of self-dual modular codes, Finite Fields and Their Applications 17 (5) (2011), 442-460.   DOI   ScienceOn
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.
10 V.S. Pless, On the uniqueness of the Golay codes, J. Combin. Theory 5 (1968), 215-228.   DOI