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The classification of self-orthogonal codes over mathbb Zp2 of lengths leq 3

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In this paper, we find all inequivalent classes of self-orthogonal codes over mathbb Zp2 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 Zp2 includes the classification of all codes over mathbb Zp. Consequently, we classify all the codes over mathbb Zp and self-orthogonal codes over mathbb Zp2 of lengths l leq3 according to the automorphism group of each code.

Abstract

In this paper, we find all inequivalent classes of self-orthogonal codes over mathbb Zp2 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 Zp2 includes the classification of all codes over mathbb Zp. Consequently, we classify all the codes over mathbb Zp and self-orthogonal codes over mathbb Zp2 of lengths l leq3 according to the automorphism group of each code.

참고문헌 (10)

  1. R.A.L. Betty, "Mass formula for self-orthogonal codes over Zp2Zp2", Journal of combinatorics, information & system sciences, 34, pp.51~66 (2009)
  2. W. Cary Huffman, "Fundamentals of error correcting codes" (2003), Cambridge University Pless
  3. W. Choi, "Self-dual codes over Zp2Zp2 of length 4", ~
  4. J.H. Conway, "Self-dual codes over the integers modulo 4", J. Comin. Theory Ser. A, 62, pp.30~45 (1993)
  5. Steven T. Dougherty, "Optimal Linear Codes over $\mathbb{Z}_m$", 대한수학회지, 44(5), pp.1139~1162 (2007), 대한수학회
  6. Y. Lee, "An efficient construction of self-dual codes", CoRR (2012)
  7. K. Nagata, "Constructive algorithm of self-dual error-correcting codes", 11th International Workshop on Algebraic and Combinatorial Coding Theory, pp.215~220 (2008)
  8. Y.H. Park, "The classification of self-dual modular codes", Finite Fields and Their Applications, 17(5), pp.442~460 (2011)
  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, pp.418~421 (1965)
  10. V.S. Pless, "On the uniqueness of the Golay codes", J. Combin. Theory, 5, pp.215~228 (1968)

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