BibTex RIS Kaynak Göster

Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$

Yıl 2015, , 163 - 168, 14.09.2015
https://doi.org/10.13069/jacodesmath.90080

Öz

In this paper, we study skew cyclic codes over the ring $R=\mathbb{F}_{q}+u\mathbb{F}_{q}+v\mathbb{F}_{q}+uv\mathbb{F}_{q}$, where $u^{2}=u,v^{2}=v,uv=vu$, $q=p^{m}$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $R$ through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length $n$ over $R.$

Kaynakça

  • T. Abualrub and P. Seneviratne, Skew codes over rings, in Proc. IMECS, Hong Kong, II, 2010.
  • F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer, 1992.
  • D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Engrg. Comm. Comput., 18(4), 379-389, 2007.
  • D. Boucher and F. Ulmer, Coding with skew polynomial ring, J. Symb. Comput., 44(12), 1644-1656, 200
  • D. Boucher, P. Sol´e and F. Ulmer, Skew constacyclic codes over Galois ring, Adv. Math. Commun., 2(3), 273-292, 2008.
  • J. Gao, Skew cyclic codes over Fp+ vFp, J. Appl. Math. Inform., 31(3,4), 337-342, 2013.
  • J. Gao, L. Z. Shen and F. W. Fu, Skew generalized quasi-cyclic codes over finite fields, arXiv preprint arXiv:1309.1621, 2013.
  • F. Gursoy, I. Siap and B. Yildiz, Construction of skew cyclic codes over Fq+ vFq, Adv. Math. Commun., 8(3), 313-322, 2014.
  • F. Hernando and D. Ruano, Sixteen new linear codes with Plotkin sum, arXiv preprint arXiv:0804.3507, 2008.
  • S. Jitman, S. Ling and P. Udomkavanich, Skew constacyclic over finite chain rings, Adv. Math. Commun., 6(1), 29-63, 2012.
  • A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The Z-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40(2), 301-319, 1994.
  • I. Siap, T. Abualrub, N. Aydin and P. Seneviratne, Skew cyclic codes of arbitrary length, Int. Nat. Sci., 2(1), 10-20, 2011.
  • Y. T. Zhang, Research on constacyclic codes over some classes of finite non-chain rings, Master’s thesis, Hefei University of Technology, 2013.
Yıl 2015, , 163 - 168, 14.09.2015
https://doi.org/10.13069/jacodesmath.90080

Öz

Kaynakça

  • T. Abualrub and P. Seneviratne, Skew codes over rings, in Proc. IMECS, Hong Kong, II, 2010.
  • F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer, 1992.
  • D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Engrg. Comm. Comput., 18(4), 379-389, 2007.
  • D. Boucher and F. Ulmer, Coding with skew polynomial ring, J. Symb. Comput., 44(12), 1644-1656, 200
  • D. Boucher, P. Sol´e and F. Ulmer, Skew constacyclic codes over Galois ring, Adv. Math. Commun., 2(3), 273-292, 2008.
  • J. Gao, Skew cyclic codes over Fp+ vFp, J. Appl. Math. Inform., 31(3,4), 337-342, 2013.
  • J. Gao, L. Z. Shen and F. W. Fu, Skew generalized quasi-cyclic codes over finite fields, arXiv preprint arXiv:1309.1621, 2013.
  • F. Gursoy, I. Siap and B. Yildiz, Construction of skew cyclic codes over Fq+ vFq, Adv. Math. Commun., 8(3), 313-322, 2014.
  • F. Hernando and D. Ruano, Sixteen new linear codes with Plotkin sum, arXiv preprint arXiv:0804.3507, 2008.
  • S. Jitman, S. Ling and P. Udomkavanich, Skew constacyclic over finite chain rings, Adv. Math. Commun., 6(1), 29-63, 2012.
  • A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The Z-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40(2), 301-319, 1994.
  • I. Siap, T. Abualrub, N. Aydin and P. Seneviratne, Skew cyclic codes of arbitrary length, Int. Nat. Sci., 2(1), 10-20, 2011.
  • Y. T. Zhang, Research on constacyclic codes over some classes of finite non-chain rings, Master’s thesis, Hefei University of Technology, 2013.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Ting Yao Bu kişi benim

Minjia Shi Bu kişi benim

Patrick Solé Bu kişi benim

Yayımlanma Tarihi 14 Eylül 2015
Yayımlandığı Sayı Yıl 2015

Kaynak Göster

APA Yao, T., Shi, M., & Solé, P. (2015). Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$. Journal of Algebra Combinatorics Discrete Structures and Applications, 2(3), 163-168. https://doi.org/10.13069/jacodesmath.90080
AMA Yao T, Shi M, Solé P. Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$. Journal of Algebra Combinatorics Discrete Structures and Applications. Eylül 2015;2(3):163-168. doi:10.13069/jacodesmath.90080
Chicago Yao, Ting, Minjia Shi, ve Patrick Solé. “Skew Cyclic Codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$”. Journal of Algebra Combinatorics Discrete Structures and Applications 2, sy. 3 (Eylül 2015): 163-68. https://doi.org/10.13069/jacodesmath.90080.
EndNote Yao T, Shi M, Solé P (01 Eylül 2015) Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$. Journal of Algebra Combinatorics Discrete Structures and Applications 2 3 163–168.
IEEE T. Yao, M. Shi, ve P. Solé, “Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 2, sy. 3, ss. 163–168, 2015, doi: 10.13069/jacodesmath.90080.
ISNAD Yao, Ting vd. “Skew Cyclic Codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$”. Journal of Algebra Combinatorics Discrete Structures and Applications 2/3 (Eylül 2015), 163-168. https://doi.org/10.13069/jacodesmath.90080.
JAMA Yao T, Shi M, Solé P. Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015;2:163–168.
MLA Yao, Ting vd. “Skew Cyclic Codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 2, sy. 3, 2015, ss. 163-8, doi:10.13069/jacodesmath.90080.
Vancouver Yao T, Shi M, Solé P. Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015;2(3):163-8.