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A class of $p$-ary cyclic codes and their weight enumerators
Cyclic and BCH codes whose minimum distance equals their maximum BCH bound
1. | Departamento de Matemáticas, Universidad de Murcia, Spain, Spain |
2. | Departamento de Ciencias Naturales y Matemáticas, Pontificia Universidad Javeriana seccional Cali, Colombia |
References:
[1] |
P. Camion, Abelian codes, MRC Tech. Sum. Rep. 1059, Univ. Wisconsin Madison, 1970. |
[2] |
P. Charpin, Open problems on cyclic codes, in Handbook of Coding Theory, North-Holland, Amsterdam, 1998, 963-1063. |
[3] |
R. T. Chien and D. M. Choy, Algebraic generalization of BCH-Goppa-Helgert codes, IEEE Trans. Inf. Theory, 21 (1975), 70-79. |
[4] |
, GAP - Groups, Algorithms, Programming - a system for computational discrete algebra, http://www.gap-system.org/ |
[5] |
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge Univ. Press, 2003.
doi: 10.1017/CBO9780511807077. |
[6] |
F. J. Macwilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1977. |
[7] |
J. H. Van Lint and R. M. Wilson, On the minimum distance of cyclic codes, IEEE Trans. Inf. Theory, 32 (1986), 23-40.
doi: 10.1109/TIT.1986.1057134. |
show all references
References:
[1] |
P. Camion, Abelian codes, MRC Tech. Sum. Rep. 1059, Univ. Wisconsin Madison, 1970. |
[2] |
P. Charpin, Open problems on cyclic codes, in Handbook of Coding Theory, North-Holland, Amsterdam, 1998, 963-1063. |
[3] |
R. T. Chien and D. M. Choy, Algebraic generalization of BCH-Goppa-Helgert codes, IEEE Trans. Inf. Theory, 21 (1975), 70-79. |
[4] |
, GAP - Groups, Algorithms, Programming - a system for computational discrete algebra, http://www.gap-system.org/ |
[5] |
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge Univ. Press, 2003.
doi: 10.1017/CBO9780511807077. |
[6] |
F. J. Macwilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1977. |
[7] |
J. H. Van Lint and R. M. Wilson, On the minimum distance of cyclic codes, IEEE Trans. Inf. Theory, 32 (1986), 23-40.
doi: 10.1109/TIT.1986.1057134. |
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