Hasse-Weil bound for additive cyclic codes

Guneri, Cem
Özbudak, Ferruh
Ozdemir, Funda
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.


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.
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...
Elements of prescribed order, prescribed traces and systems of rational functions over finite fields
Özbudak, Ferruh (Springer Science and Business Media LLC, 2005-01-01)
Let k greater than or equal to 1 and f(1),..., f(r) is an element of F-qk (x) be a system of rational functions forming a strongly linearly independent set over a finite field F-q. Let gamma(1),..., gamma(r) is an element of F-q be arbitrarily prescribed elements. We prove that for all sufficiently large extensions F-qkm, there is an element xi is an element of F-qkm of prescribed order such that Tr-Fqkm /Fq (f(i) (xi)) = gamma(i) for i = 1,..., r, where Tr-Fqkm/fq is the relative trace map from F-qkm onto ...
Systematic authentication codes using additive polynomials
Özbudak, Ferruh (Springer Science and Business Media LLC, 2008-12-01)
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.
Manguoğlu, Murat (Society for Industrial & Applied Mathematics (SIAM), 2019-01-01)
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with a relatively small number of negative eigenvalues. The proposed scheme consists of an outer minimum residual (MINRES) iteration, preconditioned by an inner conjugate gradient (CG) iteration in which CG can be further preconditioned. The robustness of the proposed scheme is illustrated by solving indefinite linear systems that arise in t...
Citation Formats
C. Guneri, F. Özbudak, and F. Ozdemir, “Hasse-Weil bound for additive cyclic codes,” DESIGNS CODES AND CRYPTOGRAPHY, pp. 249–263, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36259.