MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS
In this paper we introduce a level weight enumerator for linear binary codes whose index set is a forest. This weight enumerator gives most of the weight enumerators as a special case by specializing its variables. We provea MacWilliams identity for this weight enumerator over this special familyof posets which also generalizes the previous results in literature. Further,both the code and its dual are considered over this family of posets usingthe definition of this weight enumerator which was not possible before. We conclude by an illustrative example and some remarks
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- [1] S. Akbiyik, I. Siap, A P-Complete weight enumerator with respect to poset metric and its MacWilliams identity, (Turkish), Adiyaman University Journal of Science, 1 (1) (2011) 28ñ 39.
- [2] H.K. Kim, D.Y. Oh, A classiÖcation of posets admitting the MacWilliams identity, IEEE Transactions on Information Theory 51 (4) (2005) 1424ñ1431.
- [3] W.C. Hu§man, V.Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, 2003.
- [4] F.J. MacWilliams, N.J. Sloane, The Theory of Error- Correcting Codes, Amsterdam, The Netherlands: North- Holland, 1977.
- [5] S.T. Dougherty, M.M. Skriganov, MacWilliams Duality and the Rosenbloom-Tsfasman Metric, Mosc. Math. J. 2 (1) (2002) 81ñ97.
- [6] R.A. Brualdi, J.S. Graves, K.M. Lawrence, Codes with a poset metric, Discrete Math. 147 (1995) 57ñ72.
- [7] H. Niederreiter, Points Sets and Sequences with Small Discrepancy, Monatsh. Math. 104 (1987) 221ñ228.
- [8] H. Niederreiter, A combinatorial problem for vector spaces over Önite Öelds, Discrete Math. 96 (1991) 273ñ337.
- [9] S. Roman, Introduction to Coding and Information Theory, Springer, New York, Berlin, Heidelberg, 1997.
- [10] J. N. Gutierrez, H. Tapia-Recillas, A MacWilliams identity for poset-codes, Congr. Numer. 133 (1998) 63-73.
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi