Linking Reversed and Dual Codes of Quasi-Cyclic Codes

A SPECIAL CLASS OF QUASI-CYCLIC CODES

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972717000636 ◽

2017 ◽

Vol 96 (3) ◽

pp. 513-518 ◽

Cited By ~ 2

Author(s):

MINJIA SHI ◽

JIE TANG ◽

MAORONG GE ◽

LIN SOK ◽

PATRICK SOLÉ

Keyword(s):

Special Class ◽

Cyclic Code ◽

Cyclic Codes ◽

Dual Code ◽

Extension Field ◽

Dual Codes ◽

Lcd Codes ◽

Quasi Cyclic Codes

We study a special class of quasi-cyclic codes, obtained from a cyclic code over an extension field of the alphabet field by taking its image on a basis. When the basis is equal to its dual, the dual code admits the same construction. We give some examples of self-dual codes and LCD codes obtained in this way.

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An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes

MATEC Web of Conferences ◽

10.1051/matecconf/202133604001 ◽

2021 ◽

Vol 336 ◽

pp. 04001

Author(s):

Yu Yao ◽

Yuena Ma ◽

Husheng Li ◽

Jingjie Lv

Keyword(s):

Cyclic Codes ◽

Explicit Construction ◽

Error Correcting Codes ◽

Inner Product ◽

Quantum Codes ◽

Dual Codes ◽

Index 2 ◽

Quantum Error ◽

Hermitian Inner Product ◽

Quasi Cyclic Codes

In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes. By studying the form of Hermitian dual codes and their algebraic structure, we propose a sufficient condition for self-orthogonality of GQC codes with Hermitian inner product. By comparison, the quantum codes we constructed have better parameters than known codes.

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A class of constacyclic codes over the ring Z4[u,v]/ and their Gray images

Filomat ◽

10.2298/fil1908237i ◽

2019 ◽

Vol 33 (8) ◽

pp. 2237-2248 ◽

Cited By ~ 1

Author(s):

Habibul Islam ◽

Om Prakash

Keyword(s):

Cyclic Codes ◽

Constacyclic Codes ◽

Gray Maps ◽

Permutation Equivalent ◽

Quasi Cyclic Codes

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.

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Quantum Codes Derived from One-Generator Quasi-Cyclic Codes with Hermitian Inner Product

International Journal of Theoretical Physics ◽

10.1007/s10773-019-04324-z ◽

2019 ◽

Vol 59 (1) ◽

pp. 300-312 ◽

Cited By ~ 1

Author(s):

Jingjie Lv ◽

Ruihu Li ◽

Junli Wang

Keyword(s):

Cyclic Codes ◽

Inner Product ◽

Quantum Codes ◽

Hermitian Inner Product ◽

Quasi Cyclic Codes

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Quasi-cyclic codes over the ring 𝔽p[u]/〈u2 − u〉

Asian-European Journal of Mathematics ◽

10.1142/s1793557115500850 ◽

2015 ◽

Vol 08 (04) ◽

pp. 1550085

Author(s):

Sukhamoy Pattanayak ◽

Abhay Kumar Singh

Keyword(s):

Structural Properties ◽

Cyclic Codes ◽

Natural Generalization ◽

Spanning Set ◽

The One ◽

Quasi Cyclic Codes

Quasi-cyclic (QC) codes are a natural generalization of cyclic codes. In this paper, we study some structural properties of QC codes over [Formula: see text], where [Formula: see text] is a prime and [Formula: see text]. By exploring their structure, we determine the one generator QC codes over [Formula: see text] and the size by giving a minimal spanning set. We discuss some examples of QC codes of various length over [Formula: see text].

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Constacyclic and Linear Complementary Dual Codes Over Fq + uFq

Defence Science Journal ◽

10.14429/dsj.70.15691 ◽

2020 ◽

Vol 70 (6) ◽

pp. 626-632

Author(s):

Om Prakash ◽

Shikha Yadav ◽

Ram Krishna Verma

Keyword(s):

Cyclic Codes ◽

Gray Map ◽

Constacyclic Codes ◽

Dual Codes ◽

Gray Image ◽

New Class ◽

Sharing Scheme ◽

Lcd Codes ◽

Reversible Cyclic Codes

This article discusses linear complementary dual (LCD) codes over ℜ = Fq+uFq(u2=1) where q is a power of an odd prime p. Authors come up with a new Gray map from ℜn to F2nq and define a new class of codes obtained as the gray image of constacyclic codes over .ℜ Further, we extend the study over Euclidean and Hermitian LCD codes and establish a relation between reversible cyclic codes and Euclidean LCD cyclic codes over ℜ. Finally, an application of LCD codes in multisecret sharing scheme is given.

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