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
Construction of self dual codes from graphs
Date
2022-07-01
Author
Fellah, Nazahet
Guenda, Kenza
Özbudak, Ferruh
Seneviratne, Padmapani
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
190
views
0
downloads
Cite This
In this work we define and study binary codes C-q,C-k and (C-q,C-k) over bar obtained from neighbor- hood designs of Paley-type bipartite graphs P(q, k) and their complements, respectively for q an odd prime. We prove that for some values of q and k the codes C-q,C-k are self-dual and the codes (C-q,C-k) over bar are self-orthogonal. Most of these codes tend to be with optimal or near optimal parameters. Next, we extend the codes C(q,k )to get doubly even self dual codes and find that most of these codes are extremal.
Subject Keywords
Paley-type bipartite graphs
,
Hadamard matrices
,
Self-dual codes
,
Extremal doubly even codes
,
MATRICES
URI
https://hdl.handle.net/11511/100698
Journal
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
DOI
https://doi.org/10.1007/s00200-022-00567-2
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
LCD codes from tridiagonal Toeplitz matrices
Shi, Minjia; Özbudak, Ferruh; Xu, Li; Solé, Patrick (2021-10-01)
Double Toeplitz (DT) codes are codes with a generator matrix of the form (I,T) with T a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When T is tridiagonal and symmetric we determine its spectrum explicitly by using Dickson polynomials, and deduce from there conditions for the code to be LCD. Using a special concatenation process, we construct optimal or quasi-optimal examples of binary and ternary LCD codes from DT codes over extension fields.
Belief propagation decoding of polar codes under factor graph permutations
Peker, Ahmet Gökhan; Yücel, Melek Diker; Department of Electrical and Electronics Engineering (2018)
Polar codes, introduced by Arıkan, are linear block codes that can achieve the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. Polar codes of block length N are constructed by channel polarization method, which consists of channel combining and splitting operations to obtain N polarized subchannels from N copies of binary-input discrete memoryless channels. As N grows, symmetric channel capacities of the polarized subchannels converge to either 0 or...
Multidimensional cyclic codes and Artin–Schreier type hypersurfaces over finite fields
Güneri, Cem; Özbudak, Ferruh (Elsevier BV, 2008-1)
We obtain a trace representation for multidimensional cyclic codes via Delsarte's theorem. This relates the weights of the codewords to the number of affine rational points of Artin-Schreier type hypersurfaces over finite fields. Using Deligne's and Hasse-Weil-Serre inequalities we get bounds on the minimum distance. Comparison of the bounds is made and illustrated by examples. Some applications of our results are given. We obtain a bound on certain character sums over F-2 which gives better estimates than ...
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.
Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
N. Fellah, K. Guenda, F. Özbudak, and P. Seneviratne, “Construction of self dual codes from graphs,”
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100698.