Further improvements on asymptotic bounds for codes using distinguished divisors

Date

2007-07-01

Author

Niederreiter, Harald
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

137
views

0
downloads

For a prime power q, let alpha(q) be the standard function in the asymptotic theory of codes, that is, alpha(q)(delta) (6) is the largest asymptotic information rate that can be achieved for a given asymptotic relative minimum distance 6 of q-ary codes. In recent years the Tsfasman-VlAduj-Zink lower bound on alpha(q) (delta) was improved by Elkies, Xing, and Niederreiter and Ozbudak. In this paper we show further improvements on these bounds by using distinguished divisors of global function fields. (c) 2005 Elsevier Inc. All rights reserved.

Subject Keywords

Theoretical Computer Science, General Engineering, Algebra and Number Theory, Applied Mathematics

URI

https://hdl.handle.net/11511/47698

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/j.ffa.2005.11.004

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Improved asymptotic bounds for codes using distinguished divisors of global function fields Niederreiter, Harald; Özbudak, Ferruh (Society for Industrial & Applied Mathematics (SIAM), 2007-01-01) For a prime power q, let alpha(q) be the standard function in the asymptotic theory of codes, that is, alpha(q)(delta) is the largest asymptotic information rate that can be achieved for a given asymptotic relative minimum distance delta of q-ary codes. In recent years the Tsfasman-Vladut-Zink lower bound on alpha(q)(delta) was improved by Elkies, Xing, Niederreiter and Ozbudak, and Maharaj. In this paper we show further improvements on these bounds by using distinguished divisors of global function fields....
Uniqueness of F-q-quadratic perfect nonlinear maps from F-q3 to F-q(2) Özbudak, Ferruh (Elsevier BV, 2014-09-01) Let q be a power of an odd prime. We prove that all F-q-quadratic perfect nonlinear maps from F-q3 to F-q(2) are equivalent. We also give a geometric method to find the corresponding equivalence explicitly.
Joint linear complexity of arbitrary multisequences consisting of linear recurring sequences Fu, Fang-Wei; Niederreiter, Harald; Özbudak, Ferruh (Elsevier BV, 2009-08-01) Let g(1),..., g(s) is an element of F-q[x] be arbitrary nonconstant monic polynomials. Let M(g(1),..., g(s)) denote the set of s-fold multisequences (sigma(1),...,sigma(s)) such that sigma(i) is a linear recurring sequence over F-q with characteristic polynomial g(i) for each 1 <= i <= s. Recently, we obtained in some special cases (for instance when gl,..., gs are pairwise coprime or when g(1) = ... = g(s)) the expectation and the variance of the joint linear complexity of random multisequences that are un...
Some sufficient conditions for p-nilpotency of a finite group Kızmaz, Muhammet Yasir (Informa UK Limited, 2019-09-02) Let G be a finite group and let p be prime dividing . In this article, we supply some sufficient conditions for G to be p-nilpotent (see Theorem 1.2) as an extension of the main theorem of Li et al. (J. Group Theor. 20(1): 185-192, 2017).
A relation between quasi-cyclic codes and 2-D cyclic codes Guneri, Cem; Özbudak, Ferruh (Elsevier BV, 2012-01-01) We consider a q-ary quasi-cyclic code C of length ml and index l, where both in and l are relatively prime to q. If the constituents of C are cyclic codes, we show that C can also be viewed as a 2-D cyclic code of size m x l over F(q). In case in and l are also coprime to each other, we easily observe that the code C must be equivalent to a cyclic code, which was proved earlier by Lim.

Citation Formats

H. Niederreiter and F. Özbudak, “Further improvements on asymptotic bounds for codes using distinguished divisors,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 423–443, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47698.