Korean Journal of Mathematics

  • 제22권4호
  • /
  • Pages.725-742
  • /
  • 2014
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2014.12.01
  • 심사 : 2014.12.10
  • 발행 : 2014.12.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  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. https://doi.org/10.1016/0097-3165(93)90070-O
  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. https://doi.org/10.1016/j.ffa.2011.02.010
  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. https://doi.org/10.1016/S0021-9800(68)80067-5

피인용 문헌

  1. MASS FORMULA OF SELF-DUAL CODES OVER GALOIS RINGS GR(p2, 2) vol.24, pp.4, 2016, https://doi.org/10.11568/kjm.2016.24.4.751