Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
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
222
views
0
downloads
Cite This
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
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.