Year 2016,
Volume: 29 Issue: 4, 869 - 877, 19.12.2016
Abstract
In this paper, the MacWilliams identity is stated for codes
over quaternion integers with respect to the 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
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
| Authors | |
|---|---|
| Publication Date | December 19, 2016 |
| IZ | https://izlik.org/JA58EH58ZZ |
| Published in Issue | Year 2016 Volume: 29 Issue: 4 |