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Codes over polynomial rings and their projections
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We study codes over the polynomial ring Fq[D] and their projections to the finite rings Fq[D]/(Dm) 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.
Abstract
We study codes over the polynomial ring Fq[D] and their projections to the finite rings Fq[D]/(Dm) 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.
참고문헌 (4)
- S. T. Dougherty, "Lifted Codes and their Weight Enumerators", ~ (2004)
- R. J. McEliece, "The algebraic theory of convolutional codes, Handbook of Coding Theory", pp.1165~1138 (1998), Elsevier
- E. Rains, "Self-dual codes, Handbook of Coding Theory", pp.177~294 (1998), Elsevier
- J. A. Wood, "Duality for modules over finite rings and applications to coding theory", Amer. J. Math, 121, pp.555~575 (1999)
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