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Linear complexity of cyclotomic sequences of order six and BCH codes over GF(3)
Construction of skew cyclic codes over $\mathbb F_q+v\mathbb F_q$
1. | Department of Mathematics, Yildiz Technical University, 34210, Istanbul, Turkey, Turkey |
2. | Department of Mathematics, Fatih University, 34500, Istanbul |
References:
[1] |
T. Abualrub, A. Ghrayeb, N. Aydin and I. Siap, On the construction of skew quasi-cyclic codes, IEEE Trans. Inform. Theory, 56 (2010), 2080-2090.
doi: 10.1109/TIT.2010.2044062. |
[2] |
T. Abualrub and P. Seneviratne, Skew codes over rings, in Proc. IMECS, Hong Kong, 2010. |
[3] |
D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Eng. Comm., 18 (2007), 379-389.
doi: 10.1007/s00200-007-0043-z. |
[4] |
D. Boucher, P. Solé and F. Ulmer, Skew constacyclic codes over Galois rings, Adv. Math. Commun., 2 (2008), 273-292.
doi: 10.3934/amc.2008.2.273. |
[5] |
D. Boucher and F. Ulmer, Coding with skew polynomial rings, J. Symb. Comput., 44 (2009), 1644-1656.
doi: 10.1016/j.jsc.2007.11.008. |
[6] |
J. Gao, Skew cyclic codes over $\mathbb F_p+v\mathbb F_p$, J. Appl. Math. Inform., 31 (2013), 337-342.
doi: 10.14317/jami.2013.337. |
[7] |
A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The $\mathbb Z_4$-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40 (1994), 301-319.
doi: 10.1109/18.312154. |
[8] |
S. Jitman, S. Ling and P. Udomkavanich, Skew constacyclic codes over finite chain rings, Adv. Math. Commun., 6 (2012), 29-63.
doi: 10.3934/amc.2012.6.39. |
[9] |
B. R. McDonald, Finite Rings with Identity, Marcel Dekker Inc., New York, 1974. |
[10] |
I. Siap, T. Abualrub, N. Aydin and P. Seneviratne, Skew cyclic codes of arbitrary length, Int. J. Inform. Coding Theory, 2 (2011), 10-20.
doi: 10.1504/IJICOT.2011.044674. |
[11] |
X. Q. Xu and S. X. Zhu, Skew cyclic codes over the ring $\mathbb F_4+v\mathbb F_4$, J. Hefei Univ. Technol. Nat. Sci., 34 (2011), 1429-1432. |
[12] |
S. Zhu, Y. Wang and M. Shi, Some results on cyclic codes over $\mathbb F_2+v\mathbb F_2$, IEEE Trans. Inform. Theory, 56 (2010), 1680-1684.
doi: 10.1109/TIT.2010.2040896. |
show all references
References:
[1] |
T. Abualrub, A. Ghrayeb, N. Aydin and I. Siap, On the construction of skew quasi-cyclic codes, IEEE Trans. Inform. Theory, 56 (2010), 2080-2090.
doi: 10.1109/TIT.2010.2044062. |
[2] |
T. Abualrub and P. Seneviratne, Skew codes over rings, in Proc. IMECS, Hong Kong, 2010. |
[3] |
D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Eng. Comm., 18 (2007), 379-389.
doi: 10.1007/s00200-007-0043-z. |
[4] |
D. Boucher, P. Solé and F. Ulmer, Skew constacyclic codes over Galois rings, Adv. Math. Commun., 2 (2008), 273-292.
doi: 10.3934/amc.2008.2.273. |
[5] |
D. Boucher and F. Ulmer, Coding with skew polynomial rings, J. Symb. Comput., 44 (2009), 1644-1656.
doi: 10.1016/j.jsc.2007.11.008. |
[6] |
J. Gao, Skew cyclic codes over $\mathbb F_p+v\mathbb F_p$, J. Appl. Math. Inform., 31 (2013), 337-342.
doi: 10.14317/jami.2013.337. |
[7] |
A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The $\mathbb Z_4$-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40 (1994), 301-319.
doi: 10.1109/18.312154. |
[8] |
S. Jitman, S. Ling and P. Udomkavanich, Skew constacyclic codes over finite chain rings, Adv. Math. Commun., 6 (2012), 29-63.
doi: 10.3934/amc.2012.6.39. |
[9] |
B. R. McDonald, Finite Rings with Identity, Marcel Dekker Inc., New York, 1974. |
[10] |
I. Siap, T. Abualrub, N. Aydin and P. Seneviratne, Skew cyclic codes of arbitrary length, Int. J. Inform. Coding Theory, 2 (2011), 10-20.
doi: 10.1504/IJICOT.2011.044674. |
[11] |
X. Q. Xu and S. X. Zhu, Skew cyclic codes over the ring $\mathbb F_4+v\mathbb F_4$, J. Hefei Univ. Technol. Nat. Sci., 34 (2011), 1429-1432. |
[12] |
S. Zhu, Y. Wang and M. Shi, Some results on cyclic codes over $\mathbb F_2+v\mathbb F_2$, IEEE Trans. Inform. Theory, 56 (2010), 1680-1684.
doi: 10.1109/TIT.2010.2040896. |
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