Korean Journal of Mathematics

  • 제17권4호
  • /
  • Pages.385-397
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  • 2009
  • /
  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

CODES OVER POLYNOMIAL RINGS AND THEIR PROJECTIONS

  • Park, Young Ho (Department of Mathematics Kangwon National University)
  • 투고 : 2008.09.12
  • 발행 : 2009.12.30
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초록

We study codes over the polynomial ring ${\mathbb{F}}_q[D]$ and their projections to the finite rings ${\mathbb{F}}_q[D]/(D^m)$ and the weight enumerators of self-dual codes over these rings. We also give the formula for the number of codewords of minimum weight in the projections.

키워드

참고문헌

  1. S. T. Dougherty, S. Y. Kim, and Y. H. Park, Lifted Codes and their Weight Enumerators, submitted, 2004.
  2. R. J. McEliece, The algebraic theory of convolutional codes, Handbook of Coding Theory (V. S. Pless and W. C. Huffman, eds.), Elsevier, Amsterdam, 1998, 1165-1138.
  3. E. Rains and N. J. A. Sloane, Self-dual codes, Handbook of Coding Theory (V. S. Pless and W. C. Huffman, eds.), Elsevier, Amsterdam, 1998, 177-294.
  4. J. A. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math 121, 1999, 555-575 https://doi.org/10.1353/ajm.1999.0024