Systematic authentication codes using additive polynomials

Using additive polynomials related to some curves over finite fields, we construct two families of systematic authentication codes. We use tight bounds for the number of rational points of these curves in estimating the probabilities of the systematic authentication codes. We compare their parameters with some existing codes in the literature. We observe that the parameters are better than the existing ones in some cases.


Constructions and bounds on linear error-block codes
LİNG, San; Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-12-01)
We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert-Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over F-2. We also study the asymptotic of linear error-block codes. We define the real valued function alpha (q,m,a) (delta), which is an analog of the important real valued function alpha (q) (delta) in the asymptotic theory of classical linear error-correctin...
Improvements on generalized hamming weights of some trace codes
GÜNERİ, CEM; Özbudak, Ferruh (Springer Science and Business Media LLC, 2006-05-01)
We obtain improved bounds for the generalized Hamming weights of some trace codes which include a large class of cyclic codes over any finite field. In particular, we improve the corresponding bounds of Stichtenoth and Voss [8] using various methods altogether.
Hasse-Weil bound for additive cyclic codes
Guneri, Cem; Özbudak, Ferruh; Ozdemir, Funda (Springer Science and Business Media LLC, 2017-01-01)
We obtain a bound on the minimum distance of additive cyclic codes via the number of rational points on certain algebraic curves over finite fields. This is an extension of the analogous bound in the case of classical cyclic codes. Our result is the only general bound on such codes aside from Bierbrauer's BCH bound. We compare our bounds' performance against the BCH bound for additive cyclic codes in a special case and provide examples where it yields better results.
Tezer, Münevver (Informa UK Limited, 1989-01-01)
This paper is concerned with the evaluation of some infinite integrals involving products of exponential and Bessel functions. These integrals are transformed, through some identities, into the expressions containing modified Bessel functions. In this way, the difficulties associated with the computations of infinite integrals with oscillating integrands are eliminated.
Results on symmetric S-boxes constructed by concatenation of RSSBs
KAVUT, SELÇUK; Baloglu, Sevdenur (Springer Science and Business Media LLC, 2019-07-01)
In this paper, we first present an efficient exhaustive search algorithm to enumerate 6 x 6 bijective S-boxes with the best-known nonlinearity 24 in a class of S-boxes that are symmetric under the permutation (x) = (x(0), x(2), x(3), x(4), x(5), x(1)), where x = (x(0), x1,...,x5)?26. Since any S-box S:?26?26 in this class has the property that S((x)) = (S(x)) for every x, it can be considered as a construction obtained by the concatenation of 5 x 5 rotation-symmetric S-boxes (RSSBs). The size of the search ...
Citation Formats
F. Özbudak, “Systematic authentication codes using additive polynomials,” DESIGNS CODES AND CRYPTOGRAPHY, pp. 61–77, 2008, Accessed: 00, 2020. [Online]. Available: