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Quaternary periodic complementary/Z-complementary sequence sets based on interleaving technique and Gray mapping
Bent functions on a Galois ring and systematic authentication codes
1. | LAGA, Universities of Paris 8 and Paris 13, CNRS, Paris, France |
2. | Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, 09349, México, D.F., Mexico, Mexico |
References:
[1] |
C. Carlet, More correlation-immune and resilient functions over Galois fields and Galois rings, in "Advances in Cryptology-EUROCRYPT 97,'' 1233 (1997), 422-433. |
[2] |
C. Carlet, C. Ding and H. Niederreiter, Authentication schemes from highly nonlinear functions, Des. Codes Cryptogr., 40 (2006), 71-79.
doi: 10.1007/s10623-005-6407-0. |
[3] |
C. Carlet and S. Dubuc, On generalized bent and $q$-ary perfect nonlinear functions, in "Proceedings of the 5th conference on Finite Fields and Applications,'' Springer-Verlag, (1999), 81-94. |
[4] |
C. Ding, Systematic authentication codes from highly nonlinear functions, IEEE Trans. Inform. Theory, 50 (2004), 2421-2428.
doi: 10.1109/TIT.2004.834788. |
[5] |
E. N. Gilbert, F. J. Macwilliams and N. J. A. Sloane, Codes which detect deception, Bell Syst. Tech. J., 33 (1974), 405-424. |
[6] |
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. |
[7] |
K. Ireland and M. Rosen, "A Classical Introduction to Modern Number Theory,'' 2nd edition, Springer-Verlag, New York, 1990. |
[8] |
P. V. Kumar, R. A. Scholtz and L. R. Welch, Generalized bent functions and their properties, J. Comb. Theory, 40 (1985), 90-107.
doi: 10.1016/0097-3165(85)90049-4. |
[9] |
B. R. McDonald, "Finite Rings with Identity,'' Marcel Deckker, Inc., New York, 1974. |
[10] |
F. Özbudak and Z. Saygi, Some constructions of systematic authentication codes using Galois rings, Des. Codes Cryptogr., 41 (2006), 343-357.
doi: 10.1007/s10623-006-9021-x. |
[11] |
G. J. Simmons, Authentication theory/coding theory, in "Advances in Cryptology-Crypto 84,'' Springer-Verlag, New York, (1984), 411-431. |
[12] |
G. J. Simmons, A survey of information authentication, in "Contemporary Cryptology: The Science of Information Integrity'' (ed. G.J. Simmons), IEEE Press, New York, (1992), 379-419. |
[13] |
D. R. Stinson, "Cryptography: Theory and Practice,'' CRC Press, 1995. |
[14] |
Z.-X. Wan, "Lectures on Finite Fields and Galois Rings,'' World Scientific, 2003. |
show all references
References:
[1] |
C. Carlet, More correlation-immune and resilient functions over Galois fields and Galois rings, in "Advances in Cryptology-EUROCRYPT 97,'' 1233 (1997), 422-433. |
[2] |
C. Carlet, C. Ding and H. Niederreiter, Authentication schemes from highly nonlinear functions, Des. Codes Cryptogr., 40 (2006), 71-79.
doi: 10.1007/s10623-005-6407-0. |
[3] |
C. Carlet and S. Dubuc, On generalized bent and $q$-ary perfect nonlinear functions, in "Proceedings of the 5th conference on Finite Fields and Applications,'' Springer-Verlag, (1999), 81-94. |
[4] |
C. Ding, Systematic authentication codes from highly nonlinear functions, IEEE Trans. Inform. Theory, 50 (2004), 2421-2428.
doi: 10.1109/TIT.2004.834788. |
[5] |
E. N. Gilbert, F. J. Macwilliams and N. J. A. Sloane, Codes which detect deception, Bell Syst. Tech. J., 33 (1974), 405-424. |
[6] |
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. |
[7] |
K. Ireland and M. Rosen, "A Classical Introduction to Modern Number Theory,'' 2nd edition, Springer-Verlag, New York, 1990. |
[8] |
P. V. Kumar, R. A. Scholtz and L. R. Welch, Generalized bent functions and their properties, J. Comb. Theory, 40 (1985), 90-107.
doi: 10.1016/0097-3165(85)90049-4. |
[9] |
B. R. McDonald, "Finite Rings with Identity,'' Marcel Deckker, Inc., New York, 1974. |
[10] |
F. Özbudak and Z. Saygi, Some constructions of systematic authentication codes using Galois rings, Des. Codes Cryptogr., 41 (2006), 343-357.
doi: 10.1007/s10623-006-9021-x. |
[11] |
G. J. Simmons, Authentication theory/coding theory, in "Advances in Cryptology-Crypto 84,'' Springer-Verlag, New York, (1984), 411-431. |
[12] |
G. J. Simmons, A survey of information authentication, in "Contemporary Cryptology: The Science of Information Integrity'' (ed. G.J. Simmons), IEEE Press, New York, (1992), 379-419. |
[13] |
D. R. Stinson, "Cryptography: Theory and Practice,'' CRC Press, 1995. |
[14] |
Z.-X. Wan, "Lectures on Finite Fields and Galois Rings,'' World Scientific, 2003. |
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