On normalized generating sets for GQC codes over Z2

Sunghan Bae; Pyung Lyun Kang; Chengju Li

doi:10.1016/j.ffa.2016.11.017

On normalized generating sets for GQC codes over Z₂

Sunghan Bae, Pyung Lyun Kang, Chengju Li

Software Engineering Institute

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let r_i be positive integers and R_i=Z₂[x]/(x^r_i−1) for 1≤i≤ℓ. Denote R=R₁×R₂×⋯×R_ℓ. Generalized quasi-cyclic (GQC) code C of length (r₁,r₂,…,r_ℓ) over Z₂ can be viewed as Z₂[x]-submodule of R. In this paper, we investigate the algebraic structure of C by presenting its normalized generating set. We also present a method to determine the normalized generating set of the dual code of C, which is derived from the normalized generating set of C.

Original language	English
Pages (from-to)	285-300
Number of pages	16
Journal	Finite Fields and their Applications
Volume	45
DOIs	https://doi.org/10.1016/j.ffa.2016.11.017
State	Published - 1 May 2017

Keywords

Binary codes
Dual codes
Generalized quasi-cyclic codes

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10.1016/j.ffa.2016.11.017

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title = "On normalized generating sets for GQC codes over Z2",

abstract = "Let ri be positive integers and Ri=Z2[x]/(xri−1) for 1≤i≤ℓ. Denote R=R1×R2×⋯×Rℓ. Generalized quasi-cyclic (GQC) code C of length (r1,r2,…,rℓ) over Z2 can be viewed as Z2[x]-submodule of R. In this paper, we investigate the algebraic structure of C by presenting its normalized generating set. We also present a method to determine the normalized generating set of the dual code of C, which is derived from the normalized generating set of C.",

keywords = "Binary codes, Dual codes, Generalized quasi-cyclic codes",

author = "Sunghan Bae and Kang, \{Pyung Lyun\} and Chengju Li",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

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T1 - On normalized generating sets for GQC codes over Z2

AU - Bae, Sunghan

AU - Kang, Pyung Lyun

AU - Li, Chengju

PY - 2017/5/1

Y1 - 2017/5/1

N2 - Let ri be positive integers and Ri=Z2[x]/(xri−1) for 1≤i≤ℓ. Denote R=R1×R2×⋯×Rℓ. Generalized quasi-cyclic (GQC) code C of length (r1,r2,…,rℓ) over Z2 can be viewed as Z2[x]-submodule of R. In this paper, we investigate the algebraic structure of C by presenting its normalized generating set. We also present a method to determine the normalized generating set of the dual code of C, which is derived from the normalized generating set of C.

AB - Let ri be positive integers and Ri=Z2[x]/(xri−1) for 1≤i≤ℓ. Denote R=R1×R2×⋯×Rℓ. Generalized quasi-cyclic (GQC) code C of length (r1,r2,…,rℓ) over Z2 can be viewed as Z2[x]-submodule of R. In this paper, we investigate the algebraic structure of C by presenting its normalized generating set. We also present a method to determine the normalized generating set of the dual code of C, which is derived from the normalized generating set of C.

KW - Binary codes

KW - Dual codes

KW - Generalized quasi-cyclic codes

UR - https://www.scopus.com/pages/publications/85011811006

U2 - 10.1016/j.ffa.2016.11.017

DO - 10.1016/j.ffa.2016.11.017

M3 - 文章

AN - SCOPUS:85011811006

SN - 1071-5797

VL - 45

SP - 285

EP - 300

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

On normalized generating sets for GQC codes over Z₂

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