Yıl 2016,
Cilt: 29 Sayı: 4, 869 - 877, 19.12.2016
Öz
In this paper, the MacWilliams identity is stated for codes
over quaternion integers with respect to the Lipschitz metric.
Anahtar Kelimeler
MacWilliams identity Block codes Weight enumerator Lipschitz metric.
Kaynakça
- 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.
Yıl 2016,
Cilt: 29 Sayı: 4, 869 - 877, 19.12.2016
Öz
Kaynakça
- 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.
Toplam 29 adet kaynakça vardır.
Ayrıntılar
| Bölüm | Mathematics |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 19 Aralık 2016 |
| Yayımlandığı Sayı | Yıl 2016 Cilt: 29 Sayı: 4 |