Further results on Euclidean and Hermitian linear complementary dual codes

Zihui Liu; Jie Wang

doi:10.1016/j.ffa.2019.05.005

Further results on Euclidean and Hermitian linear complementary dual codes

Zihui Liu^*, Jie Wang

^*此作品的通讯作者

数学学院

Peking University

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

By using the cogredience theories of an alternate matrix, a symmetric matrix and a Hermitian-symmetric matrix, we will find a special family of generator matrices for any linear code, and then using the special family of generator matrices, we will provide a general method to construct a linear complementary dual (LCD) code (resp. a Hermitian LCD code) from any given linear code. Still using the special family of generator matrices for LCD codes (resp. Hermitian LCD codes), we will present the enumeration of all [n,k] LCD codes (resp. Hermitian LCD codes).

源语言	英语
页（从-至）	104-133
页数	30
期刊	Finite Fields and their Applications
卷	59
DOI	https://doi.org/10.1016/j.ffa.2019.05.005
出版状态	已出版 - 9月 2019

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title = "Further results on Euclidean and Hermitian linear complementary dual codes",

abstract = "By using the cogredience theories of an alternate matrix, a symmetric matrix and a Hermitian-symmetric matrix, we will find a special family of generator matrices for any linear code, and then using the special family of generator matrices, we will provide a general method to construct a linear complementary dual (LCD) code (resp. a Hermitian LCD code) from any given linear code. Still using the special family of generator matrices for LCD codes (resp. Hermitian LCD codes), we will present the enumeration of all [n,k] LCD codes (resp. Hermitian LCD codes).",

keywords = "Alternate matrix, Cogredience transformation, Hermitian LCD codes, Hermitian-symmetric matrix, LCD codes, Symmetric matrix",

author = "Zihui Liu and Jie Wang",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = sep,

doi = "10.1016/j.ffa.2019.05.005",

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T1 - Further results on Euclidean and Hermitian linear complementary dual codes

AU - Liu, Zihui

AU - Wang, Jie

PY - 2019/9

Y1 - 2019/9

N2 - By using the cogredience theories of an alternate matrix, a symmetric matrix and a Hermitian-symmetric matrix, we will find a special family of generator matrices for any linear code, and then using the special family of generator matrices, we will provide a general method to construct a linear complementary dual (LCD) code (resp. a Hermitian LCD code) from any given linear code. Still using the special family of generator matrices for LCD codes (resp. Hermitian LCD codes), we will present the enumeration of all [n,k] LCD codes (resp. Hermitian LCD codes).

AB - By using the cogredience theories of an alternate matrix, a symmetric matrix and a Hermitian-symmetric matrix, we will find a special family of generator matrices for any linear code, and then using the special family of generator matrices, we will provide a general method to construct a linear complementary dual (LCD) code (resp. a Hermitian LCD code) from any given linear code. Still using the special family of generator matrices for LCD codes (resp. Hermitian LCD codes), we will present the enumeration of all [n,k] LCD codes (resp. Hermitian LCD codes).

KW - Alternate matrix

KW - Cogredience transformation

KW - Hermitian LCD codes

KW - Hermitian-symmetric matrix

KW - LCD codes

KW - Symmetric matrix

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DO - 10.1016/j.ffa.2019.05.005

M3 - Article

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SN - 1071-5797

VL - 59

SP - 104

EP - 133

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

Further results on Euclidean and Hermitian linear complementary dual codes

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