Cyclic codes and reducible additive equations

Date

2007-02-01

Author

Guneri, Cem
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

157
views

0
downloads

We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Woffmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over F-p and F-p2, where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocquenghem (BCH) bound and that it yields the exact minimum distance in some cases.

Subject Keywords

Library and Information Sciences, Information Systems, Computer Science Applications

URI

https://hdl.handle.net/11511/46926

Journal

IEEE TRANSACTIONS ON INFORMATION THEORY

DOI

https://doi.org/10.1109/tit.2006.889001

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

An improvement on the bounds of Weil exponential sums over Gallois rings with some applications Ling, S; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2004-10-01) We present an upper bound for Weil-type exponential sums over Galois rings of characteristic p(2) which improves on the analog of the Weil-Carlitz-Uchiyama bound for Galois rings obtained by Kumar, Helleseth, and Calderbank. A more refined bound, expressed in terms of genera of function fields, and an analog of McEliece's theorem on the divisibility of the homogeneous weights of codewords in trace codes over Z(p)2, are also derived. These results lead to an improvement on the estimation of the minimum dista...
On Linear Complementary Pairs of Codes CARLET, Claude; Guneri, Cem; Özbudak, Ferruh; Ozkaya, Buket; SOLE, Patrick (Institute of Electrical and Electronics Engineers (IEEE), 2018-10-01) We study linear complementary pairs (LCP) of codes (C, D), where both codes belong to the same algebraic code family. We especially investigate constacyclic and quasicyclic LCP of codes. We obtain characterizations for LCP of constacyclic codes and LCP of quasi-cyclic codes. Our result for the constacyclic complementary pairs extends the characterization of linear complementary dual (LCD) cyclic codes given by Yang and Massey. We observe that when C and I) are complementary and constacyclic, the codes C and...
Periodic solutions of the hybrid system with small parameter Akhmet, Marat; Ergenc, T. (Elsevier BV, 2008-06-01) In this paper we investigate the existence and stability of the periodic solutions of a quasilinear differential equation with piecewise constant argument. The continuous and differentiable dependence of the solutions on the parameter and the initial value is considered. A new Gronwall-Bellman type lemma is proved. Appropriate examples are constructed.
Weil-Serre Type Bounds for Cyclic Codes GÜNERİ, CEM; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2008-12-01) We give a new method in order to obtain Weil-Serre type hounds on the minimum distance of arbitrary cyclic codes over F(pe) of length coprime to p, where e >= 1 is an arbitrary integer. In an earlier paper we obtained Weil-Serre type bounds for such codes only when e = 1 or e = 2 using lengthy explicit factorizations, which seems hopeless to generalize. The new method avoids such explicit factorizations and it produces an effective alternative. Using our method we obtain Weil-Serre type bounds in various ca...
Constructing linear unequal error protection codes from algebraic curves Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2003-06-01) We show that the concept of "generalized algebraic geometry codes" which was recently introduced by Xing, Niederreiter, and Lam gives a natural framework for constructing linear unequal error protection codes.

Citation Formats

C. Guneri and F. Özbudak, “Cyclic codes and reducible additive equations,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 848–853, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46926.