Construction of quasi-cyclic self-dual codes

Çomak, Pınar
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 construction of quasi-cyclic self-dual codes, especially binary cubic ones. With a new algebraic approach, binary quasi-cyclic codes of length 3l over a fi eld are defi ned by the linear codes of length l over the ring F2 XF4. İn this thesis, we improve the result for the cubic self-dual binary codes, by fi nding two new self-dual codes with the algebraic approach.


The Concatenated Structure of Quasi-Cyclic Codes and an Improvement of Jensen's Bound
Guneri, Cem; Özbudak, Ferruh (2013-02-01)
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 constit...
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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...
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...
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Guneri, Cem; Özbudak, Ferruh; Ozkaya, Buket; Sacikara, Elif; SEPASDAR, Zahra; SOLÉ, Patrick (2017-09-01)
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder Theorem yields a decomposition of GQC codes into a sum of concatenated codes. This decomposition leads to a trace formula, a minimum distance bound, and to a criteria for the GQC code to be self-dual or to be linear complementary dual (LCD). Explicit long GQC codes that ar...
Constructions and bounds on linear error-block codes
LİNG, San; Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-12-01)
We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert-Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over F-2. We also study the asymptotic of linear error-block codes. We define the real valued function alpha (q,m,a) (delta), which is an analog of the important real valued function alpha (q) (delta) in the asymptotic theory of classical linear error-correctin...
Citation Formats
P. Çomak, “Construction of quasi-cyclic self-dual codes,” M.S. - Master of Science, Middle East Technical University, 2013.