Cyclic and constacyclic codes over a non-chain ring
Cyclic and constacyclic codes over a non-chain ring
In this study, we consider linear and especially cyclic codes over the non-chain ring Zp[v]/ vp− vwhere p is a prime. This is a generalization of the case p = 3. Further, in this work the structure ofconstacyclic codes are studied as well. This study takes advantage mainly from a Gray map whichpreserves the distance between codes over this ring and p-ary codes and moreover this map enlightensthe structure of these codes. Furthermore, a MacWilliams type identity is presented together withsome illustrative examples
Keywords:
Non-chain rings, Linear codes, Cyclic codes Constacycllic codes, MacWilliams type identity,
___
- T. Abualrub, I. Siap, On the Construction of Cyclic Codes over the Ring Z2+ uZ2, WSEAS Trans. on Math., 5(6), 750-756, 2006.
- T. Abulraub, I. Siap, Cyclic Codes over the Rings Z2+ uZ and Z+ uZ2+ u2Z2, Designs, Codes and Cryptography, 3(42), 273-287, 2007.
- M. Al-Ashker, M. Hamoudeh, Cyclic codes over Z2+ uZ2+ u2Z2+ · · · + uk−1Z2, Turkish J. Math., 35(4), 737-749, 2011.
- A. Bayram, I. Siap, Structure of Codes over the Ring Z3[v]/ v3− v , Applicable Algebra in Engi- neering, Communication and Computing, 24(5), 369-386, 2013.
- K. Betsumiya, M. Harada, Optimal self-dual codes over F× F, with respect to the Hamming weight, IEEE Transactions on Information Theory, 50(2), 356-358, 2004.
- A. Bonnecaze and P. Udaya, Cyclic codes and self-dual codes over F2+uF2, IEEE Trans. Inf. Theory, 45(4), 1250-1255, 1999.
- S.T. Dougherty, B. Yildiz and S. Karadeniz, Codes over R, Gray Maps and their Binary Images, Finite Fields and Their Applications, 17(3), 205-219, 2011.
- J. Gao, Y. Wang, Some results on linear codes over Fp+ vFp+ v3Fp, Journal of Applied Mathematics and Computing, May 2014.
- A.R. Hammons, Jr., P.V. Kumar, A.R. Calderbank, N.J.A. Sloane, and P. Sole, The Z4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inf. Theory, 40(2), 301-319, 1994.
- F.J. MacWilliams and N.J.A. Sloane, The Theory of Error Correcting Codes, North-Holland, Ams- terdam, The Netherlands, 1977.
- M. Ozen and I. Siap, Linear Codes Over Fq[u]/(us) with Respect to the Rosenbloom-Tsfasman Metric, Designs, Codes and Cryptography, 38(1), 17-29, 2006.
- Y. H. Park, Modular independence and generator matrices for codes over Zm, Des. Codes Crypt., 50(2), 147-162, 2009.
- J.-F. Qian, L.-N. Zhang, and S.-X. Zhu, Constacyclic and Cyclic Codes over F+ uF2+ uF, IEICE Trans. Fundamentals, 89(6), 1863-1865, 2006.
- B. Yildiz, S. Karadeniz, Linear Codes over F2+ uF2+ vF+ uvF, Des. Codes Crypt., 54(1), 61-81, 20 B. Yildiz, S. Karadeniz, Cyclic Codes over F2+ uF+ vF+ uvF2, Des. Codes Crypt., 58(3), 221-234, 20 S.-X. Zhu, Y. Wang, M.-J. Shi, Cyclic codes over F+ vF2, ISIT’09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory, 3, 1719-1722, 2009.
- Başlangıç: 2015
- Yayıncı: İrfan ŞİAP
Sayıdaki Diğer Makaleler
Horizontal runs in domino tilings
Kamilla Oliver, Helmut Prodinger
The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes
Some Properties of topological pressure on cellular automata
New extremal binary self-dual codes of length 68