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

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University

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

9 Citations (Scopus)

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).

Original language	English
Pages (from-to)	104-133
Number of pages	30
Journal	Finite Fields and their Applications
Volume	59
DOIs	https://doi.org/10.1016/j.ffa.2019.05.005
Publication status	Published - Sept 2019

Keywords

Alternate matrix
Cogredience transformation
Hermitian LCD codes
Hermitian-symmetric matrix
LCD codes
Symmetric matrix

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10.1016/j.ffa.2019.05.005

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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",

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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

UR - http://www.scopus.com/inward/record.url?scp=85066480961&partnerID=8YFLogxK

U2 - 10.1016/j.ffa.2019.05.005

DO - 10.1016/j.ffa.2019.05.005

M3 - Article

AN - SCOPUS:85066480961

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

Abstract

Keywords

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