On self-dual and LCD quasi-twisted codes of index two over a special chain ring

Qian, Liqin; Shi, Minjia; Solé, Patrick

doi:10.1007/s12095-018-0322-5

Cited by 16 publications

(10 citation statements)

References 24 publications

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“…On the other side, double circulant LCD codes over Z 4 in [22], Z p 2 in [10] and Galois ring in [23] were studied, respectively. Further, for some related studies on these topics, interested readers can see [20,24,26,27,29]. Therefore, because of available works on non-chain rings [21,28], it is logical to investigate these codes over other semi-local non-chain rings.…”

Section: Introductionmentioning

confidence: 99%

Self-dual and LCD double circulant and double negacirculant codes over $${\mathbb {F}}_q+u{\mathbb {F}}_q+v{\mathbb {F}}_q$$

Yadav

Islam

Prakash

et al. 2021

J. Appl. Math. Comput.

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Let q be an odd prime power, and denote by F q the finite field with q elements. In this paper, we consider the ring R = F q + uF q + vF q , where u 2 = u, v 2 = v, uv = vu = 0 and study double circulant and double negacirculant codes over this ring. We first obtain the necessary and sufficient conditions for a double circulant code to be self-dual (resp. LCD). Then we enumerate self-dual and LCD double circulant and double negacirculant codes over R. Last but not the least, we show that the family of Gray images of self-dual and LCD double circulant codes over R are good. Several numerical examples of self-dual and LCD codes over F 5 as the Gray images of these codes over R are given in short lengths.

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Section: Introductionmentioning

confidence: 99%

Self-dual and LCD double circulant and double negacirculant codes over $${\mathbb {F}}_q+u{\mathbb {F}}_q+v{\mathbb {F}}_q$$

Yadav

Islam

Prakash

et al. 2021

J. Appl. Math. Comput.

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“…We start with an example where d L > d J > d Spec and the code is optimal since it reaches the best-possible minimum distance. The [21,6,8] 2 QC code with (m, , r) = (7, 3, 1), generator polynomials x 4 + x 3 + x + 1, x 4 + 1, and x 3 + x, and generator matrix…”

Section: Numerical Comparisonsmentioning

confidence: 99%

“…Quasi-twisted (QT) codes form an important class of block codes that includes cyclic codes, quasi-cyclic (QC) codes and constacyclic codes as special subclasses. In addition to their rich algebraic structure ( [16], [26]), QT codes are also known to be asymptotically good ( [8], [9], [30]) and they yield good parameters ( [1], [2], [21], [24]).…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Distance Bounds for Quasi-Twisted Codes

Ezerman

Lampos

Ling

et al. 2021

IEEE Trans. Inform. Theory

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Spectral bounds on the minimum distance of quasitwisted codes over finite fields are proposed, based on eigenvalues of polynomial matrices and the corresponding eigenspaces. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a way similar to how the Roos and shift bounds extend the BCH and HT bounds for cyclic codes. The eigencodes of a quasi-twisted code in the spectral theory and the outer codes in its concatenated structure are related. A comparison based on this relation verifies that the Jensen bound always outperforms the spectral bound under special conditions, which yields a similar relation between the Lally and the spectral bounds. The performances of the Lally, Jensen and spectral bounds are presented in comparison with each other.

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“…A double circulant self-dual code employs one generator matrix consists of two circulant matrices and possesses many good algebraic properties [5,3]. With more new double circulant self-dual codes were presented, these provide a remarkable way to construct self-dual codes [3,13,4,12,9,10,11]. Recently, by constructting double circulant generator matrixes using cyclotomy of order four modulo an odd prime p, Zhang and Ge presented some double circulant self-dual codes with optimal minimum distances [13].…”

Section: Introductionmentioning

confidence: 99%

Double Circulant Self-dual Codes on Sextic Cyclotomy

Yan¹,

Wang²,

Gao³

et al. 2020

Preprint

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This paper contributes to construct double circulant self-dual codes by sextic cyclotomy. Generator matrixes of a family of pure double circulant codes and a family of double circulant codes with boundary are formed from sextic cyclotomic classes. These codes are proved to be self-dual on certain conditions. Moreover, experiments show that some of them are optimal self-dual codes or best than ever codes over GF(2) and GF(4).

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On self-dual and LCD quasi-twisted codes of index two over a special chain ring

Cited by 16 publications

References 24 publications

Self-dual and LCD double circulant and double negacirculant codes over $${\mathbb {F}}_q+u{\mathbb {F}}_q+v{\mathbb {F}}_q$$

Self-dual and LCD double circulant and double negacirculant codes over $${\mathbb {F}}_q+u{\mathbb {F}}_q+v{\mathbb {F}}_q$$

A Comparison of Distance Bounds for Quasi-Twisted Codes

Double Circulant Self-dual Codes on Sextic Cyclotomy

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