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MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS

Year 2013, Volume: 62 Issue: 1, 61 - 71, 01.02.2013
https://doi.org/10.1501/Commua1_0000000686

Abstract

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

References

  • [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.
Year 2013, Volume: 62 Issue: 1, 61 - 71, 01.02.2013
https://doi.org/10.1501/Commua1_0000000686

Abstract

References

  • [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.
There are 10 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Seda Akbıyık This is me

İrfan Siap This is me

Publication Date February 1, 2013
Published in Issue Year 2013 Volume: 62 Issue: 1

Cite

APA Akbıyık, S., & Siap, İ. (2013). MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 62(1), 61-71. https://doi.org/10.1501/Commua1_0000000686
AMA Akbıyık S, Siap İ. MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2013;62(1):61-71. doi:10.1501/Commua1_0000000686
Chicago Akbıyık, Seda, and İrfan Siap. “MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62, no. 1 (February 2013): 61-71. https://doi.org/10.1501/Commua1_0000000686.
EndNote Akbıyık S, Siap İ (February 1, 2013) MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62 1 61–71.
IEEE S. Akbıyık and İ. Siap, “MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 62, no. 1, pp. 61–71, 2013, doi: 10.1501/Commua1_0000000686.
ISNAD Akbıyık, Seda - Siap, İrfan. “MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62/1 (February 2013), 61-71. https://doi.org/10.1501/Commua1_0000000686.
JAMA Akbıyık S, Siap İ. MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62:61–71.
MLA Akbıyık, Seda and İrfan Siap. “MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 62, no. 1, 2013, pp. 61-71, doi:10.1501/Commua1_0000000686.
Vancouver Akbıyık S, Siap İ. MACWILLIAMS IDENTITIES OVER SOME SPECIAL POSETS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62(1):61-7.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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