Gilbert Varshamov type bounds for linear codes over finite chain rings

Date

2007-02-01

Author

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

159
views

0
downloads

We obtain finite and asymptotic Gilbert-Varshamov type bounds for linear codes over finite chain rings with various weights.

Subject Keywords

Computer Networks and Communications, Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics

URI

https://hdl.handle.net/11511/46966

Journal

Advances In Mathematics Of Communications

DOI

https://doi.org/10.3934/amc.2007.1.99

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Generalized nonbinary sequences with perfect autocorrelation, flexible alphabets and new periods BOZTAŞ, Serdar; Özbudak, Ferruh; TEKİN, Eda (Springer Science and Business Media LLC, 2018-05-01) We extend the parameters and generalize existing constructions of perfect autocorrelation sequences over complex alphabets. In particular, we address the PSK+ constellation (Boztas and Udaya 2010) and present an extended number theoretic criterion which is sufficient for the existence of the new sequences with perfect autocorrelation. These sequences are shown to exist for nonprime alphabets and more general lengths in comparison to existing designs. The new perfect autocorrelation sequences provide novel a...
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.
On affine variety codes from the Klein quartic Geil, Olav; Özbudak, Ferruh (Springer Science and Business Media LLC, 2019-03-01) We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433-464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and HOholdt, IEEE Trans. Inform. The...
Value sets of Lattes maps over finite fields Küçüksakallı, Ömer (Elsevier BV, 2014-10-01) We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
Fibre products of Kummer covers and curves with many points Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-10-01) We study the general fibre product of any two Kummer covers of the projective line over finite fields. Under some assumptions, we obtain an involved condition for the existence of rational points in the fibre product over a rational point of the projective line so that we determine the exact number of the rational points. Using this, we construct explicit examples of such fibre products with many rational points. In particular we obtain a record and a new entry for the table (http://www.science.uva.nl/(simi...

Citation Formats

F. Özbudak, “Gilbert Varshamov type bounds for linear codes over finite chain rings,” Advances In Mathematics Of Communications, pp. 99–109, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46966.