Cyclic and constacyclic codes over a non-chain ring

Ayşegül Bayram; Irfan Siap

doi:10.13069/jacodesmath.31486

Cyclic and constacyclic codes over a non-chain ring

Yıl 2014, Cilt: 1 Sayı: 1, 1 - 12, 01.03.2014

Ayşegül Bayram , Irfan Siap

https://doi.org/10.13069/jacodesmath.31486

Cited By: 11

Öz

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

Anahtar Kelimeler

Non-chain rings, Linear codes, Cyclic codes, Constacycllic codes, MacWilliams type identity

Kaynakça

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.

Yıl 2014, Cilt: 1 Sayı: 1, 1 - 12, 01.03.2014

Ayşegül Bayram , Irfan Siap

https://doi.org/10.13069/jacodesmath.31486

Cited By: 11

Öz

Kaynakça

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.

Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Makaleler
Yazarlar	Ayşegül Bayram Irfan Siap
Yayımlanma Tarihi	1 Mart 2014
Yayımlandığı Sayı	Yıl 2014 Cilt: 1 Sayı: 1

Kaynak Göster

APA	Bayram, A., & Siap, I. (2014). Cyclic and constacyclic codes over a non-chain ring. Journal of Algebra Combinatorics Discrete Structures and Applications, 1(1), 1-12. https://doi.org/10.13069/jacodesmath.31486
AMA	Bayram A, Siap I. Cyclic and constacyclic codes over a non-chain ring. Journal of Algebra Combinatorics Discrete Structures and Applications. Mart 2014;1(1):1-12. doi:10.13069/jacodesmath.31486
Chicago	Bayram, Ayşegül, ve Irfan Siap. “Cyclic and Constacyclic Codes over a Non-Chain Ring”. Journal of Algebra Combinatorics Discrete Structures and Applications 1, sy. 1 (Mart 2014): 1-12. https://doi.org/10.13069/jacodesmath.31486.
EndNote	Bayram A, Siap I (01 Mart 2014) Cyclic and constacyclic codes over a non-chain ring. Journal of Algebra Combinatorics Discrete Structures and Applications 1 1 1–12.
IEEE	A. Bayram ve I. Siap, “Cyclic and constacyclic codes over a non-chain ring”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 1, sy. 1, ss. 1–12, 2014, doi: 10.13069/jacodesmath.31486.
ISNAD	Bayram, Ayşegül - Siap, Irfan. “Cyclic and Constacyclic Codes over a Non-Chain Ring”. Journal of Algebra Combinatorics Discrete Structures and Applications 1/1 (Mart 2014), 1-12. https://doi.org/10.13069/jacodesmath.31486.
JAMA	Bayram A, Siap I. Cyclic and constacyclic codes over a non-chain ring. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014;1:1–12.
MLA	Bayram, Ayşegül ve Irfan Siap. “Cyclic and Constacyclic Codes over a Non-Chain Ring”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 1, sy. 1, 2014, ss. 1-12, doi:10.13069/jacodesmath.31486.
Vancouver	Bayram A, Siap I. Cyclic and constacyclic codes over a non-chain ring. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014;1(1):1-12.