On complementary-dual quasi-cyclic codes

Esmaeili, Morteza; Yari, Somaye

doi:10.1016/j.ffa.2009.01.002

Cited by 75 publications

(53 citation statements)

References 8 publications

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“…Moreover, the [77, 11,32] code attains the current known lower bound on the minimum distance of both QC and linear codes ( [8,16]). Remark 6.1.…”

Section: Binary Qc Codes Of Rate 1/3mentioning

confidence: 97%

“…To the best of our knowledge only a few LCD QC codes are known, [11]. This link between E(s 2 )-optimal supersaturated designs and LCD QC codes enables us to retrieve those supersaturated designs from [28,30] for which the restrictions of the previous theorem hold, in order to generate new QC codes in the class of LCD QC codes.…”

Section: Theorem 47mentioning

confidence: 99%

“…Furthermore, the practical utility of LCD codes was demonstrated in [33]. Recently, Esmaeilli and Yari identified few classes of LCD quasi-cyclic codes in [11].…”

Section: Introductionmentioning

confidence: 99%

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Quasi-Cyclic Codes From Cyclic-Structured Designs With Good Properties

Koukouvinos

Simos

2011

Discrete Math. Algorithm. Appl.

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In this paper, one-generator binary quasi-cyclic (QC) codes are explored by statistical tools derived from design of experiments. A connection between a structured cyclic class of statistical designs, k-circulant supersaturated designs and QC codes is given. The mathematical structure of the later codes is explored and a link between complementary dual binary QC codes and E(s 2 )-optimal k-circulant supersaturated designs is established. Moreover, binary QC codes of rate 1/3, 1/4, 1/5, 1/6 and 1/7 are found by utilizing a genetic algorithm. Our approach is based on a search for good or best codes that attain the current best-known lower bounds on the minimum distance of linear codes, formulated as a combinatorial optimization problem. Surveying previous results, it is shown, that our codes reach the current best-known lower bounds on the minimum distance of linear codes with the same parameters.

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“…Moreover, the [77, 11,32] code attains the current known lower bound on the minimum distance of both QC and linear codes ( [8,16]). Remark 6.1.…”

Section: Binary Qc Codes Of Rate 1/3mentioning

confidence: 97%

Section: Theorem 47mentioning

confidence: 99%

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Quasi-Cyclic Codes From Cyclic-Structured Designs With Good Properties

Koukouvinos

Simos

2011

Discrete Math. Algorithm. Appl.

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“…Esmaeiliand Yari in [9] studied complementary-dual quasi-cyclic codes. Necessary and sufficient conditions for certain classes of quasi-cyclic codes to be LCD codes were obtained [9]. Dougherty, Kim, Ozkaya, Sok and Solé developed a linear programming bound on the largest size of an LCD code of given length and minimum distance [8].…”

Section: Introductionmentioning

confidence: 99%

Galois LCD codes over finite fields

Liu

Fan

Liu

2018

Finite Fields and Their Applications

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In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and constacyclic codes to be Galois LCD codes are characterized. Some illustrative examples which constacyclic codes are Galois LCD MDS codes are provided as well. In particular, we study Hermitian LCD constacyclic codes. Finally, we present a construction of a class of Hermitian LCD codes which are also MDS codes.

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“…Later, Sendrier showed that LCD codes meet the asymptotic Gilbert-Varshamov bound using the hull dimension spectra of linear codes [16]. In the literature, LCD codes have been studied extensively and many results and properties for LCD cyclic codes were found [6], [7], [10], [14], [19], [13], [20]. In [8], the problem of constructing LCD MDS codes over finite fields of even characteristic was solved.…”

Section: Introductionmentioning

confidence: 99%

Explicit MDS Codes With Complementary Duals

Beelen

Jin

2018

IEEE Trans. Inform. Theory

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In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on. LCD codes have been extensively studied in literature. On the other hand, MDS codes form an optimal family of classical codes which have wide applications in both theory and practice. The main purpose of this paper is to give an explicit construction of several classes of LCD MDS codes, using tools from algebraic function fields. We exemplify this construction and obtain several classes of explicit LCD MDS codes for the odd characteristic case.

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On complementary-dual quasi-cyclic codes

Cited by 75 publications

References 8 publications

Quasi-Cyclic Codes From Cyclic-Structured Designs With Good Properties

Quasi-Cyclic Codes From Cyclic-Structured Designs With Good Properties

Galois LCD codes over finite fields

Explicit MDS Codes With Complementary Duals

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