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

225
views

0
downloads

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

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...
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...
New cubic self-dual codes of length 54, 60 and 66 Comak, PINAR; Kim, Jon Lark; Özbudak, Ferruh (2018-08-01) We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length with the algebraic approach of Ling and Sol, (IEEE Trans Inf Theory 47(7):2751-2760, 2001. doi:. In particular, we improve the previous results by constructing 1 new binary [54, 27, 10], 6 new [60, 30, 12] and 50 new [66, 33, 12] cubic self-dual codes. We conjecture that there exist no more binary cubic self-dual codes with length 54, 60 and 66.
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...

Citation Formats

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.