Constructions and bounds on linear error-block codes

Özbudak, Ferruh
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-correcting codes. We obtain both Gilbert-Varshamov and algebraic geometry type lower bounds on alpha (q,m,a) (delta). We compare these lower bounds in graphs.


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.
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.
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.
Global existence and boundedness for a class of second-order nonlinear differential equations
Tiryaki, Aydin; Zafer, Ağacık (Elsevier BV, 2013-09-01)
In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form
Differential quadrature solution of nonlinear reaction-diffusion equation with relaxation-type time integration
Meral, G.; Tezer, Münevver (Informa UK Limited, 2009-01-01)
This paper presents the combined application of differential quadrature method (DQM) and finite-difference method (FDM) with a relaxation parameter to nonlinear reaction-diffusion equation in one and two dimensions. The polynomial-based DQM is employed to discretize the spatial partial derivatives by using Gauss-Chebyshev-Lobatto points. The resulting system of ordinary differential equations is solved, discretizating the time derivative by an explicit FDM. A relaxation parameter is used to position the sol...
Citation Formats
S. LİNG and F. Özbudak, “Constructions and bounds on linear error-block codes,” DESIGNS CODES AND CRYPTOGRAPHY, pp. 297–316, 2007, Accessed: 00, 2020. [Online]. Available: