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Existence conditions for self-orthogonal negacyclic codes over finite fields
1. | Department of Physical Science and Technology, Central China Normal University, Wuhan, Hubei 430079, China |
2. | School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China |
3. | School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637616, Singapore |
References:
[1] |
G. K. Bakshi and M. Raka, Self-dual and self-orthogonal negacyclic codes of length $2p^n$ over a finite field, Finite Fields Appl., 19 (2013), 39-54.
doi: 10.1016/j.ffa.2012.10.003. |
[2] |
T. Blackford, Negacyclic duadic codes, Finite Fields Appl., 14 (2008), 930-943.
doi: 10.1016/j.ffa.2008.05.004. |
[3] |
I. F. Blake, S. Gao and R. C. Mullin, Explicit factorization of $X^{2^k}+1$ over $F_p$ with prime $p\equiv3 (mod 4)$, Appl. Algebra Engrg. Comm. Comput., 4 (1993), 89-94.
doi: 10.1007/BF01386832. |
[4] |
H. Q. Dinh, Repeated-root constacyclic codes of length $2p^s$, Finite Fields Appl., 18 (2012) 133-143.
doi: 10.1016/j.ffa.2011.07.003. |
[5] |
H. Q. Dinh, Structure of repeated-root constacyclic codes of length $3p^s$ and their duals, Discrete Math., 313 (2013), 983-991.
doi: 10.1016/j.disc.2013.01.024. |
[6] |
W. Fu and T. Feng, On self-orthogonal group ring codes, Designs Codes Crypt., 50 (2009), 203-214.
doi: 10.1007/s10623-008-9224-4. |
[7] |
W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl., 11 (2005), 451-490.
doi: 10.1016/j.ffa.2005.05.012. |
[8] |
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, Cambridge, 2003. |
[9] |
Y. Jia, S. Ling and C. Xing, On self-dual cyclic codes over finite fields, IEEE Trans. Inf. Theory, 57 (2011), 2243-2251.
doi: 10.1109/TIT.2010.2092415. |
[10] |
X. Kai and S. Zhu, On cyclic self-dual codes, Appl. Algebra Engrg. Comm. Comput., 19 (2008), 509-525.
doi: 10.1007/s00200-008-0086-9. |
[11] |
L. Kathuria and M. Raka, Existence of cyclic self-orthogonal codes: a note on a result of Vera Pless, Adv. Math. Commun., 6 (2012), 499-503.
doi: 10.3934/amc.2012.6.499. |
[12] |
R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, Cambridge, 2008. |
[13] |
V. Pless, Cyclotomy and cyclic codes, the unreasonable effectiveness of number theory, in Proc. Sympos. Appl. Math., Amer. Math. Soc., 1992, 91-104. |
[14] |
N. J. A. Sloane and J. G. Thompson, Cyclic self-dual codes, IEEE Trans. Inf. Theory, 29 (1983), 364-367.
doi: 10.1109/TIT.1983.1056682. |
[15] |
Z. Wan, Lectures on Finite Fields and Galois Rings, World Scientific Publishing, 2003. |
[16] |
W. Willems, A note on self-dual group codes, IEEE Trans. Inf. Theory, 48 (2002), 3107-3109.
doi: 10.1109/TIT.2002.805076. |
show all references
References:
[1] |
G. K. Bakshi and M. Raka, Self-dual and self-orthogonal negacyclic codes of length $2p^n$ over a finite field, Finite Fields Appl., 19 (2013), 39-54.
doi: 10.1016/j.ffa.2012.10.003. |
[2] |
T. Blackford, Negacyclic duadic codes, Finite Fields Appl., 14 (2008), 930-943.
doi: 10.1016/j.ffa.2008.05.004. |
[3] |
I. F. Blake, S. Gao and R. C. Mullin, Explicit factorization of $X^{2^k}+1$ over $F_p$ with prime $p\equiv3 (mod 4)$, Appl. Algebra Engrg. Comm. Comput., 4 (1993), 89-94.
doi: 10.1007/BF01386832. |
[4] |
H. Q. Dinh, Repeated-root constacyclic codes of length $2p^s$, Finite Fields Appl., 18 (2012) 133-143.
doi: 10.1016/j.ffa.2011.07.003. |
[5] |
H. Q. Dinh, Structure of repeated-root constacyclic codes of length $3p^s$ and their duals, Discrete Math., 313 (2013), 983-991.
doi: 10.1016/j.disc.2013.01.024. |
[6] |
W. Fu and T. Feng, On self-orthogonal group ring codes, Designs Codes Crypt., 50 (2009), 203-214.
doi: 10.1007/s10623-008-9224-4. |
[7] |
W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl., 11 (2005), 451-490.
doi: 10.1016/j.ffa.2005.05.012. |
[8] |
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, Cambridge, 2003. |
[9] |
Y. Jia, S. Ling and C. Xing, On self-dual cyclic codes over finite fields, IEEE Trans. Inf. Theory, 57 (2011), 2243-2251.
doi: 10.1109/TIT.2010.2092415. |
[10] |
X. Kai and S. Zhu, On cyclic self-dual codes, Appl. Algebra Engrg. Comm. Comput., 19 (2008), 509-525.
doi: 10.1007/s00200-008-0086-9. |
[11] |
L. Kathuria and M. Raka, Existence of cyclic self-orthogonal codes: a note on a result of Vera Pless, Adv. Math. Commun., 6 (2012), 499-503.
doi: 10.3934/amc.2012.6.499. |
[12] |
R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, Cambridge, 2008. |
[13] |
V. Pless, Cyclotomy and cyclic codes, the unreasonable effectiveness of number theory, in Proc. Sympos. Appl. Math., Amer. Math. Soc., 1992, 91-104. |
[14] |
N. J. A. Sloane and J. G. Thompson, Cyclic self-dual codes, IEEE Trans. Inf. Theory, 29 (1983), 364-367.
doi: 10.1109/TIT.1983.1056682. |
[15] |
Z. Wan, Lectures on Finite Fields and Galois Rings, World Scientific Publishing, 2003. |
[16] |
W. Willems, A note on self-dual group codes, IEEE Trans. Inf. Theory, 48 (2002), 3107-3109.
doi: 10.1109/TIT.2002.805076. |
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