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

11 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

Access to Document

10.1016/j.ffa.2019.05.005

Cite this

@article{cda9601c2a964e0cbc141cde5267e795,

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",

language = "English",

volume = "59",

pages = "104--133",

journal = "Finite Fields and their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

}

TY - JOUR

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 - https://www.scopus.com/pages/publications/85066480961

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

Access to Document

Other files and links

Fingerprint

Cite this