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AN IDENTITY BETWEEN THE m-SPOTTY ROSENBLOOM-TSFASMAN WEIGHT ENUMERATORS OVER FINITE COMMUTATIVE FROBENIUS RINGS

Minjia Shi|Mehmet ¨ Ozen|Vedat S¸iap
대한수학회 (The Korean Mathematical Society)|2015.05|대한수학회보 (Bulletin of the KMS)|제52권 제3호|pp. 809-823

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참고문헌

키워드

MacWilliams identitybyte error-control codesm-spotty byte errorweight enumerators
주제분류수학

초록

This paper is devoted to presenting a MacWilliams type identity for m-spotty RT weight enumerators of byte error control codes over finite commutative Frobenius rings, which can be used to determine the error-detecting and error-correcting capabilities of a code. This provides the relation between the m-spotty RT weight enumerator of the code and that of the dual code. We conclude the paper by giving three illustrations of the results.

Abstract

This paper is devoted to presenting a MacWilliams type identity for m-spotty RT weight enumerators of byte error control codes over finite commutative Frobenius rings, which can be used to determine the error-detecting and error-correcting capabilities of a code. This provides the relation between the m-spotty RT weight enumerator of the code and that of the dual code. We conclude the paper by giving three illustrations of the results.

참고문헌 (22)

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  9. M. ¨Ozen, "The MacWilliams identity for m-spotty Rosenbloom-Tsfasman weight enumer-ator", J. Franklin Inst, 351(2), pp.743~750 (2014)
  10. L. Panek, "Classification of Niederreiter-Rosenbloom-Tsfasman block codes", IEEE Trans. Inform. Theory, 56(10), pp.5207~5216 (2010)
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  15. , ~
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  18. V. S¸iap, "A MacWilliams Type identity for m-spotty Rosenbloom-Tsfasman weight enumerators over Frobenius rings", CMMSE 2013: Proceedings of the 13th International Conference on Mathematical Methods in Science and Engineering, pp.1236~1241 (2013)
  19. K. Suzuki, "MacWilliams identity for m-spotty weight enumerator", IEICE-Tran. Fund. Elec. Comm & Comp. Sci, E93-A(2), pp.526~531 (2010)
  20. K. Suzuki, "A general class of m-spotty weight enumer-ator", IEICE-Tran. Fund. Elec. Comm & Comp. Sci, E90-A(7), pp.1418~1427 (2007)
  21. G. Umanesan, "A class of random multiple bits in a byte error correcting and single byte error detecting (St", bEC-SbED) codes, 2003, pp.52(7), 835~847
  22. J. Wood, "Duality for modules over finite rings and application to coding theory", Amer. J. Math, 121(3), pp.555~575 (1999)

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