Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
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
The Concatenated Structure of Quasi-Cyclic Codes and an Improvement of Jensen's Bound
Date
2013-02-01
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
29
views
0
downloads
Cite This
Following Jensen's work from 1985, a quasi-cyclic code can be written as a direct sum of concatenated codes, where the inner codes are minimal cyclic codes and the outer codes are linear codes. We observe that the outer codes are nothing but the constituents of the quasi-cyclic code in the sense of Ling-Sole. This concatenated structure enables us to recover some earlier results on quasi-cyclic codes in a simple way, including one of our recent results which says that a quasi-cyclic code with cyclic constituent codes are 2-D cyclic codes. In fact, we obtain a generalization of this result to multidimensional cyclic codes. The concatenated structure also yields a lower bound on the minimum distance of quasi-cyclic codes, as noted by Jensen, which we call Jensen's bound. We show that a recent lower bound on the minimum distance of quasi-cyclic codes that we obtained is in general better than Jensen's lower bound.
Subject Keywords
Concatenation
,
Constituents
,
Jensen's Bound
,
Multidimensional Cyclic Code
,
Quasi-Cyclic (QC) Code
URI
https://hdl.handle.net/11511/36691
Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
DOI
https://doi.org/10.1109/tit.2012.2225823
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
The Minimum Hamming Distance of Cyclic Codes of Length 2ps
ÖZADAM, Hakan; Özbudak, Ferruh (2009-06-12)
We study cyclic codes of length 2p(s) over F-q where p is an odd prime. Using the results of [1], we compute the minimum Hamming distance of these codes.
Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
Lopez-Permouth, Sergio R.; Ozadam, Hakan; Özbudak, Ferruh; SZABO, Steve (2013-01-01)
Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p(a), m) and generating sets for its ideals are considered. It is shown that these generating sets are strong Groebner bases. A method for finding such sets in the case that a = 2 is given. This explicitly gives the Hamming distance of all cyclic codes of le...
Construction of quasi-cyclic self-dual codes
Çomak, Pınar; Özbudak, Ferruh; Kim, Jon-Lark; Department of Cryptography (2013)
Quasi-cyclic and self-dual codes are interesting classes of linear codes. Quasi-cyclic codes are linear codes which takes maximum possible value of minimum distance among the codes with the same length and same dimension. Another class of interesting linear codes is the self-dual codes. Self-dual codes have close connections with group theory, lattice theory and design theory. There has been an active research on the classi fication of self-dual codes over fi nite fi elds and over rings. We study on constru...
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...
A survey on quaternary codes and their binary images
Özkaya, Derya; Yücel, Melek D; Department of Cryptography (2009)
Certain nonlinear binary codes having at least twice as many codewords as any known linear binary code can be regarded as the binary images of linear codes over Z4. This vision leads to a new concept in coding theory, called the Z4-linearity of binary codes. This thesis is a survey on the linear quaternary codes and their binary images under the Gray map. The conditions for the binary image of a linear quaternary code to be linear are thoroughly investigated and the Z4-linearity of the Reed-Muller and Hammi...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
C. Guneri and F. Özbudak, “The Concatenated Structure of Quasi-Cyclic Codes and an Improvement of Jensen’s Bound,”
IEEE TRANSACTIONS ON INFORMATION THEORY
, pp. 979–985, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36691.