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MacWilliams identity for linear codes over finite chain rings with respect to homogeneous weight

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In this paper, we obtain the MacWilliams identity for linear codes over finite chain rings with respect to homogeneous weight, and the product of chain rings.

Abstract

In this paper, we obtain the MacWilliams identity for linear codes over finite chain rings with respect to homogeneous weight, and the product of chain rings.

참고문헌 (10)

  1. J. Borges, "Linear and cyclic codes over direct product of finite chain rings", Mathematical Methods in the Applied Sciences, 41(16), pp.6519~6529 (2018), Wiley[DOI]
  2. W. Heise, "Weighted modules and representations of codes", Proc. Int. Workshop on Algebraic and Combinatorial Coding Theory, pp.123~129 (1998)
  3. Xiusheng Liu, "Macwilliams identities of linear codes over the ring F 2 + uF 2 + vF 2", Journal of Systems Science and Complexity, 28(3), pp.691~701 (2015), Springer Science and Business Media LLC[DOI]
  4. Jessie Macwilliams, "A Theorem on the Distribution of Weights in a Systematic Code†", Bell System Technical Journal, 42(1), pp.79~94 (1963), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
  5. F. J. MacWilliams, "The theory of error-correcting codes. II" (1977), NorthHolland Publishing Co
  6. Graham H. Norton, "On the Structure of Linear and Cyclic Codes over a Finite Chain Ring", Applicable Algebra in Engineering, Communication and Computing, 10(6), pp.489~506 (2000), Springer Science and Business Media LLC[DOI]
  7. Minjia Shi, "On ZpZpk -additive codes and their duality", IEEE Transactions on Information Theory, 65(6), pp.3841~3847 (2019), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
  8. Z. Wan, "Quaternary Codes" (1997), World Scientific
  9. J. A. Wood, "Duality for modules over finite rings and applications to coding theory", Amer. J. Math, 121(3), pp.555~575 (1999)
  10. Bahattin Yildiz, "Linear codes overZ4+uZ4: MacWilliams identities, projections, and formally self-dual codes", Finite Fields and Their Applications, 27, pp.24~40 (2014), Elsevier BV[DOI]

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