The condition for a cyclic code to have a complementary dual

Yang, Xiang; Massey, James L.

doi:10.1016/0012-365x(94)90283-6

Cited by 194 publications

(115 citation statements)

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“…It is known [9] that a q-ary cyclic code C , whose length N is relatively prime to the characteristic p of F q , is a reversible code if and only if it is an LCD code. Surprisingly, a maximal binary index-2 QC code C is reversible if and only if C = C ⊥ .…”

Section: X) Then C Is An Lcd Code If and Only Ifmentioning

confidence: 99%

“…Yang and Massey [9] showed that the necessary and sufficient condition for a length-N cyclic code C to be an LCD code is that the generator polynomial g(x) of C be self-reciprocal and all the monic irreducible factors of g(x) have the same multiplicity in g(x) as in x N − 1. Also, they proved a q-ary cyclic code, whose length N is relatively prime to the characteristic p of F q , is an LCD code if and only if it is a reversible code.…”

Section: Introductionmentioning

confidence: 99%

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On complementary-dual quasi-cyclic codes

Esmaeili

Yari

2009

Finite Fields and Their Applications

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A linear code C is said to be a complementary-dual code (an LCDThis paper is to identify few classes of LCD quasi-cyclic (QC) codes. A sufficient condition for a ρ-generator QC code C is given under which C is an LCD code. Another sufficient condition is given for maximal 1-generator codes. We provide two necessary and sufficient conditions for a maximal 1-generator QC code C satisfying certain constraints to be an LCD code. It is shown that unlike cyclic codes, a maximal 1-generator index-2 QC code is reversible if and only if it is a self-dual code. Several classes of LCD QC codes are introduced.

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Section: X) Then C Is An Lcd Code If and Only Ifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On complementary-dual quasi-cyclic codes

Esmaeili

Yari

2009

Finite Fields and Their Applications

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“…Carlet and Guilley shown an application of LCD codes against side-channel attacks and fault injection attacks, and presented several constructions of LCD codes [4]. Cyclic LCD codes over finite fields are also referred as reversible codes, Yang and Massey gave a necessary and sufficient condition for a cyclic code to have a complementary dual [26] and proved that reversible cyclic codes over finite fields are LCD codes. In [21], Massey showed that some cyclic LCD codes over finite fields are BCH codes, and also constructed reversible convolutional codes which are in fact LCD codes.…”

Section: Introductionmentioning

confidence: 99%

Do non-free LCD codes over finite commutative Frobenius rings exist?

Bhowmick

Fotue-Tabue

Martı́nez-Moro

et al. 2020

Des. Codes Cryptogr.

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In this paper, we clarify some aspects on LCD codes in the literature. We first prove that a non-free LCD code does not exist over finite commutative Frobenius local rings. We then obtain a necessary and sufficient condition for the existence of LCD code over finite commutative Frobenius rings. We later show that a free constacyclic code over finite chain ring is LCD if and only if it is reversible, and also provide a necessary and sufficient condition for a constacyclic code to be reversible over finite chain rings. We illustrate the minimum Lee-distance of LCD codes over some finite commutative chain rings and demonstrate the results with examples. We also got some new optimal 4 codes of different lengths which are cyclic LCD codes over 4 .

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“…Sendrier showed that LCD codes meet the asymptotic Gilbert-Varshamov bound over the finite fields [2]. Yang and Maseey gave a necessary and sufficient condition for a cyclic code to be LCD over finite fields [3]. After that, there are many literatures on the construction of LCD codes over finite fields [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%