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Maximum weight spectrum codes
1. | Dept. of Mathematics and Statistics, University of New Brunswick Saint John, Saint John, NB, E5S 2A6, Canada |
2. | Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland |
In the recent work [
References:
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T. L. Alderson and A. A. Bruen,
Coprimitive sets and inextendable codes, Des. Codes Cryptogr., 47 (2008), 113-124.
doi: 10.1007/s10623-007-9079-0. |
[2] |
S. Ball, Finite Geometry and Combinatorial Applications, volume 82. Cambridge University Press, 2015.
doi: 10.1017/CBO9781316257449. |
[3] |
P. Delsarte,
Four fundamental parameters of a code and their combinatorial significance, Information and Control, 23 (1973), 407-438.
doi: 10.1016/S0019-9958(73)80007-5. |
[4] |
H. Enomoto, P. Frankl, N. Ito and K. Nomura,
Codes with given distances, Graphs and Combinatorics, 3 (1987), 25-38.
doi: 10.1007/BF01788526. |
[5] |
A. Haily and D. Harzalla,
On binary linear codes whose automorphism group is trivial, Journal of Discrete Mathematical Sciences and Cryptography, 18 (2015), 495-512.
doi: 10.1080/09720529.2014.927650. |
[6] |
J. MacWilliams,
A theorem on the distribution of weights in a systematic code, The Bell System Technical Journal, 42 (1963), 79-94.
doi: 10.1002/j.1538-7305.1963.tb04003.x. |
[7] |
J. T. Schwartz,
Fast probabilistic algorithms for verification of polynomial identities, Journal of the ACM (JACM), 27 (1980), 701-717.
doi: 10.1145/322217.322225. |
[8] |
M. Shi, X. Li, A. Neri and P. Solé, How many weights can a cyclic code have?, arXiv: 1807.08418, 15, November, 2018. Google Scholar |
[9] |
M. Shi, H. Zhu, P. Solé and G. D. Cohen, How many weights can a linear code have?, Des. Codes Cryptogr., (2018).
doi: 10.1007/s10623-018-0488-z. |
[10] |
D. Slepian,
A class of binary signaling alphabets, Bell Labs Technical Journal, 35 (1956), 203-234.
doi: 10.1002/j.1538-7305.1956.tb02379.x. |
[11] |
M. A. Tsfasman and S. G. Vlăduţ, Algebraic-geometric Codes, volume 58 of Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1991. Translated from the Russian by the authors.
doi: 10.1007/978-94-011-3810-9. |
[12] |
O. Veblen and J. W. Young, Projective Geometry, Vol. 1, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1965. |
show all references
References:
[1] |
T. L. Alderson and A. A. Bruen,
Coprimitive sets and inextendable codes, Des. Codes Cryptogr., 47 (2008), 113-124.
doi: 10.1007/s10623-007-9079-0. |
[2] |
S. Ball, Finite Geometry and Combinatorial Applications, volume 82. Cambridge University Press, 2015.
doi: 10.1017/CBO9781316257449. |
[3] |
P. Delsarte,
Four fundamental parameters of a code and their combinatorial significance, Information and Control, 23 (1973), 407-438.
doi: 10.1016/S0019-9958(73)80007-5. |
[4] |
H. Enomoto, P. Frankl, N. Ito and K. Nomura,
Codes with given distances, Graphs and Combinatorics, 3 (1987), 25-38.
doi: 10.1007/BF01788526. |
[5] |
A. Haily and D. Harzalla,
On binary linear codes whose automorphism group is trivial, Journal of Discrete Mathematical Sciences and Cryptography, 18 (2015), 495-512.
doi: 10.1080/09720529.2014.927650. |
[6] |
J. MacWilliams,
A theorem on the distribution of weights in a systematic code, The Bell System Technical Journal, 42 (1963), 79-94.
doi: 10.1002/j.1538-7305.1963.tb04003.x. |
[7] |
J. T. Schwartz,
Fast probabilistic algorithms for verification of polynomial identities, Journal of the ACM (JACM), 27 (1980), 701-717.
doi: 10.1145/322217.322225. |
[8] |
M. Shi, X. Li, A. Neri and P. Solé, How many weights can a cyclic code have?, arXiv: 1807.08418, 15, November, 2018. Google Scholar |
[9] |
M. Shi, H. Zhu, P. Solé and G. D. Cohen, How many weights can a linear code have?, Des. Codes Cryptogr., (2018).
doi: 10.1007/s10623-018-0488-z. |
[10] |
D. Slepian,
A class of binary signaling alphabets, Bell Labs Technical Journal, 35 (1956), 203-234.
doi: 10.1002/j.1538-7305.1956.tb02379.x. |
[11] |
M. A. Tsfasman and S. G. Vlăduţ, Algebraic-geometric Codes, volume 58 of Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1991. Translated from the Russian by the authors.
doi: 10.1007/978-94-011-3810-9. |
[12] |
O. Veblen and J. W. Young, Projective Geometry, Vol. 1, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1965. |
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