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Some constacyclic codes over finite chain rings
1. | Faculty of Mathematics, USTHB, Algiers, Algeria |
2. | Faculty of Mathematics, University of Science and Technology, USTHB, Algeria |
3. | Department of Electrical and Computer Engineering, University of Victoria, PO Box 1700, STN CSC, Victoria, BC, Canada |
References:
[1] |
A. Batoul, K. Guenda and T. A. Gulliver, On self-dual cyclic codes over finite chain rings, Des. Codes Cryptogr., 70 (2014), 347-358.
doi: 10.1007/s10623-012-9696-0. |
[2] |
H. Dinh, On the linear ordering of some classes of negacyclic and cyclic codes and their distributions, Finite Fields Appl., 14 (2008), 22-40.
doi: 10.1016/j.ffa.2007.07.001. |
[3] |
H. Dinh and S. R. López-Permouth, Cyclic and negacyclic codes over finite chain rings, IEEE Trans. Inform. Theory, 50 (2004), 1728-1744.
doi: 10.1109/TIT.2004.831789. |
[4] |
S. T. Dougherty, J. L. Kim and H. Liu, Construction of self-dual codes over finite commutative chain rings, Int. J. Inform. Coding Theory, 1 (2010), 171-190.
doi: 10.1504/IJICoT.2010.032133. |
[5] |
G. D. Forney, N. J. A. Sloane and M. Trott, The Nordstrom-Robinson code is the binary image of the octacode, in DIMACS/IEEE Workshop Coding Quantiz., Amer. Math. Soc., 1993. |
[6] |
M. Greferath and S. E. Shmidt, Finite-ring combinatorics and Macwilliam's equivalence theorem, J. Combin. Theory A, 92 (2000), 17-28.
doi: 10.1006/jcta.1999.3033. |
[7] |
K. Guenda and T. A. Gulliver, MDS and self-dual codes over rings, Finite Fields Appl., 18 (2012), 1061-1075.
doi: 10.1016/j.ffa.2012.09.003. |
[8] |
K. Guenda and T. A. Gulliver, Self-dual repeated root cyclic and negacyclic codes over finite fields, in Proc. IEEE Int. Symp. Inform. Theory, Boston, 2012, 2904-2908.
doi: 10.1109/ISIT.2012.6284057. |
[9] |
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge Univ. Press, New York, 2003.
doi: 10.1017/CBO9780511807077. |
[10] |
P. Kanwar and S. R. López-Permouth, Cyclic codes over the integers modulo $p^m$, Finite Fields Appl., 3 (1997), 334-352.
doi: 10.1006/ffta.1997.0189. |
[11] |
S. R. López-Permouth and S. Szabo, Repeated root cyclic and negacyclic codes over Galois rings, in Appl. Alg. Eng. Com. Comp., Springer-Verlag, New York, 2009, 219-222.
doi: 10.3934/amc.2009.3.409. |
[12] |
F. J. MacWilliams, Combinatorial Properties of Elementary Abelian Groups, Ph.D. thesis, Radcliffe College, Cambridge, MA, 1962. |
[13] |
B. R. McDonald, Finite Rings with Identity, Marcel Dekker, New York, 1974. |
[14] |
A. A. Nechaev and T. Khonol'd, Weighted modules and representations of codes (in Russian), Probl. Peredachi Inform., 35 (1999), 18-39; translation in Problems Inform. Transm., 35 (1999), 205-223. |
[15] |
G. H. Norton and A. Sălăgean, On the structure of linear and cyclic codes over a finite chain ring, Appl. Algebra Engr. Comm. Comput., 10 (2000), 489-506.
doi: 10.1007/PL00012382. |
[16] |
J. Wood, Extension theorems for linear codes over finite rings, in Appl. Alg. Eng. Com. Comp. (eds. T. Mora and H. Matson), Springer-Verlag, New York, 1997, 329-340.
doi: 10.1007/3-540-63163-1_26. |
show all references
References:
[1] |
A. Batoul, K. Guenda and T. A. Gulliver, On self-dual cyclic codes over finite chain rings, Des. Codes Cryptogr., 70 (2014), 347-358.
doi: 10.1007/s10623-012-9696-0. |
[2] |
H. Dinh, On the linear ordering of some classes of negacyclic and cyclic codes and their distributions, Finite Fields Appl., 14 (2008), 22-40.
doi: 10.1016/j.ffa.2007.07.001. |
[3] |
H. Dinh and S. R. López-Permouth, Cyclic and negacyclic codes over finite chain rings, IEEE Trans. Inform. Theory, 50 (2004), 1728-1744.
doi: 10.1109/TIT.2004.831789. |
[4] |
S. T. Dougherty, J. L. Kim and H. Liu, Construction of self-dual codes over finite commutative chain rings, Int. J. Inform. Coding Theory, 1 (2010), 171-190.
doi: 10.1504/IJICoT.2010.032133. |
[5] |
G. D. Forney, N. J. A. Sloane and M. Trott, The Nordstrom-Robinson code is the binary image of the octacode, in DIMACS/IEEE Workshop Coding Quantiz., Amer. Math. Soc., 1993. |
[6] |
M. Greferath and S. E. Shmidt, Finite-ring combinatorics and Macwilliam's equivalence theorem, J. Combin. Theory A, 92 (2000), 17-28.
doi: 10.1006/jcta.1999.3033. |
[7] |
K. Guenda and T. A. Gulliver, MDS and self-dual codes over rings, Finite Fields Appl., 18 (2012), 1061-1075.
doi: 10.1016/j.ffa.2012.09.003. |
[8] |
K. Guenda and T. A. Gulliver, Self-dual repeated root cyclic and negacyclic codes over finite fields, in Proc. IEEE Int. Symp. Inform. Theory, Boston, 2012, 2904-2908.
doi: 10.1109/ISIT.2012.6284057. |
[9] |
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge Univ. Press, New York, 2003.
doi: 10.1017/CBO9780511807077. |
[10] |
P. Kanwar and S. R. López-Permouth, Cyclic codes over the integers modulo $p^m$, Finite Fields Appl., 3 (1997), 334-352.
doi: 10.1006/ffta.1997.0189. |
[11] |
S. R. López-Permouth and S. Szabo, Repeated root cyclic and negacyclic codes over Galois rings, in Appl. Alg. Eng. Com. Comp., Springer-Verlag, New York, 2009, 219-222.
doi: 10.3934/amc.2009.3.409. |
[12] |
F. J. MacWilliams, Combinatorial Properties of Elementary Abelian Groups, Ph.D. thesis, Radcliffe College, Cambridge, MA, 1962. |
[13] |
B. R. McDonald, Finite Rings with Identity, Marcel Dekker, New York, 1974. |
[14] |
A. A. Nechaev and T. Khonol'd, Weighted modules and representations of codes (in Russian), Probl. Peredachi Inform., 35 (1999), 18-39; translation in Problems Inform. Transm., 35 (1999), 205-223. |
[15] |
G. H. Norton and A. Sălăgean, On the structure of linear and cyclic codes over a finite chain ring, Appl. Algebra Engr. Comm. Comput., 10 (2000), 489-506.
doi: 10.1007/PL00012382. |
[16] |
J. Wood, Extension theorems for linear codes over finite rings, in Appl. Alg. Eng. Com. Comp. (eds. T. Mora and H. Matson), Springer-Verlag, New York, 1997, 329-340.
doi: 10.1007/3-540-63163-1_26. |
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