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THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS

Year 2016, Volume: 29 Issue: 4, 869 - 877, 19.12.2016

Murat Güzeltepe

Abstract

In this paper, the MacWilliams identity is stated for codes
over quaternion integers with respect to the Lipschitz metric.

Keywords

MacWilliams identity Block codes Weight enumerator Lipschitz metric.

References

  • F. J. MacWilliams, ”Combinatorial Problems of Elementary Abelian Groups,” Ph.D.
  • dissertation, Harvard Univ., Cambridge, MA, 1962.
  • F. J. MacWilliams, ”A theorem on the distribution of weights in a systematic code,”
  • Bell Syst. Tech. J., vol. 42, pp. 79-94, 1963.
  • F. J. Macwilliams and N. J. Sloane, ”The Theory of Error Correcting Codes”, North
  • Holland Pub. Co., 1977.
  • S. Irfan, ”MacWilliams identity for m− spotty Lee weight enumerators,” Appl. Math.
  • Lett., 23 (2010) 13-16.
  • B. Yildiz and S. Karadeniz., ”Linear codes over F2 + uF2 + vF2 + uvF2,” Des. Codes
  • Cryptogr., (2010) 54:6181.
  • J. A. Wood, Duality for modules over finite rings and applications to coding theory,
  • Amer. J. Math. 121 (1999), 555575.
  • T. Honold and I. Landjev, MacWilliams Identities for codes over frobenius ring, Finite
  • Fields and application Springer pp. 276-292, 2000.
  • V. Zinoviev, T. Ericson, On Fourier-Invariant Partitions of Finite Abelian Groups and
  • the MacWilliams Identity for Group Codes, Problems of Information Transmission, 32,
  • No. 1, 1996.
  • K. Huber, ”The MacWilliams Theorem for Two-Dimensional Modulo Metrics,”
  • AAECC, 41-48, 1997.
  • C. Martinez, E. Stafford, R. Beivide and E. Gabidulin. ”Perfect Codes over Lipschitz
  • Integers”. IEEE Int. Symposium on Information Theory, ISIT’07.
  • C. Martinez, R. Beivide, and E. M. Gabidulin, ”Perfect Codes from Cayley Graphs over
  • Lipschitz Integers,” IEEE Trans. Inform.Theory, vol. 55, pp. 3552-3562, August, 2009.
  • G. Davidoff, P. Sarnak, A. Valette, ”Elementary Number Theory, Group Theory, and
  • Ramanujan Graphs”, Cambridge University Pres, 2003.
  • M. G¨uzeltepe, ”Codes over Hurwitz integers”, Vol. 313/5, pp. 704-714, 2013.
  • M. G¨uzeltepe, O. Heden, ”Perfect Mannheim, Lipschitz and Hurwitz weight codes”,
  • Math. Communications, Vol. 19/2 pp. 253-276, 2014.
  • O. Heden, M. G¨uzeltepe, ”On perfect 1-E error-correcting codes”, Math. Communications, Vol. 20/1 pp. 23-35, 2015.

Year 2016, Volume: 29 Issue: 4, 869 - 877, 19.12.2016

Murat Güzeltepe

Abstract

References

  • F. J. MacWilliams, ”Combinatorial Problems of Elementary Abelian Groups,” Ph.D.
  • dissertation, Harvard Univ., Cambridge, MA, 1962.
  • F. J. MacWilliams, ”A theorem on the distribution of weights in a systematic code,”
  • Bell Syst. Tech. J., vol. 42, pp. 79-94, 1963.
  • F. J. Macwilliams and N. J. Sloane, ”The Theory of Error Correcting Codes”, North
  • Holland Pub. Co., 1977.
  • S. Irfan, ”MacWilliams identity for m− spotty Lee weight enumerators,” Appl. Math.
  • Lett., 23 (2010) 13-16.
  • B. Yildiz and S. Karadeniz., ”Linear codes over F2 + uF2 + vF2 + uvF2,” Des. Codes
  • Cryptogr., (2010) 54:6181.
  • J. A. Wood, Duality for modules over finite rings and applications to coding theory,
  • Amer. J. Math. 121 (1999), 555575.
  • T. Honold and I. Landjev, MacWilliams Identities for codes over frobenius ring, Finite
  • Fields and application Springer pp. 276-292, 2000.
  • V. Zinoviev, T. Ericson, On Fourier-Invariant Partitions of Finite Abelian Groups and
  • the MacWilliams Identity for Group Codes, Problems of Information Transmission, 32,
  • No. 1, 1996.
  • K. Huber, ”The MacWilliams Theorem for Two-Dimensional Modulo Metrics,”
  • AAECC, 41-48, 1997.
  • C. Martinez, E. Stafford, R. Beivide and E. Gabidulin. ”Perfect Codes over Lipschitz
  • Integers”. IEEE Int. Symposium on Information Theory, ISIT’07.
  • C. Martinez, R. Beivide, and E. M. Gabidulin, ”Perfect Codes from Cayley Graphs over
  • Lipschitz Integers,” IEEE Trans. Inform.Theory, vol. 55, pp. 3552-3562, August, 2009.
  • G. Davidoff, P. Sarnak, A. Valette, ”Elementary Number Theory, Group Theory, and
  • Ramanujan Graphs”, Cambridge University Pres, 2003.
  • M. G¨uzeltepe, ”Codes over Hurwitz integers”, Vol. 313/5, pp. 704-714, 2013.
  • M. G¨uzeltepe, O. Heden, ”Perfect Mannheim, Lipschitz and Hurwitz weight codes”,
  • Math. Communications, Vol. 19/2 pp. 253-276, 2014.
  • O. Heden, M. G¨uzeltepe, ”On perfect 1-E error-correcting codes”, Math. Communications, Vol. 20/1 pp. 23-35, 2015.
There are 29 citations in total.

Details

Journal Section Mathematics
Authors

Murat Güzeltepe

Publication Date December 19, 2016
Published in Issue Year 2016 Volume: 29 Issue: 4

Cite

APA Güzeltepe, M. (2016). THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS. Gazi University Journal of Science, 29(4), 869-877.
AMA Güzeltepe M. THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS. Gazi University Journal of Science. December 2016;29(4):869-877.
Chicago Güzeltepe, Murat. “THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS”. Gazi University Journal of Science 29, no. 4 (December 2016): 869-77.
EndNote Güzeltepe M (December 1, 2016) THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS. Gazi University Journal of Science 29 4 869–877.
IEEE M. Güzeltepe, “THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS”, Gazi University Journal of Science, vol. 29, no. 4, pp. 869–877, 2016.
ISNAD Güzeltepe, Murat. “THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS”. Gazi University Journal of Science 29/4 (December2016), 869-877.
JAMA Güzeltepe M. THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS. Gazi University Journal of Science. 2016;29:869–877.
MLA Güzeltepe, Murat. “THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS”. Gazi University Journal of Science, vol. 29, no. 4, 2016, pp. 869-77.
Vancouver Güzeltepe M. THE MACWILLIAMS IDENTITY FOR LIPSCHITZ WEIGHT ENUMERATORS. Gazi University Journal of Science. 2016;29(4):869-77.