Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지

CODES OVER POLYNOMIAL RINGS AND THEIR PROJECTIONS

  • Park, Young Ho (Department of Mathematics Kangwon National University)
  • Received : 2008.09.12
  • Published : 2009.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  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