Half-cyclic, dihedral and half-dihedral codes

R. Jajcay; P. Potočnik; S. Wilson

doi:10.1007/s12190-020-01374-z

Half-cyclic, dihedral and half-dihedral codes

R. Jajcay, P. Potočnik, S. Wilson

Mathematics and Statistics

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

1 Scopus citations

Abstract

This note discusses, in elementary terms, linear codes over Z₂ which are closed under 2-step cyclic shifts, and classifies them in terms of special linear combinations of polynomials. Codes which are preserved under order-reversing automorphisms are also discussed, and a classification result in terms of special linear combinations of polynomials is obtained.

Original language	English (US)
Pages (from-to)	691-708
Number of pages	18
Journal	Journal of Applied Mathematics and Computing
Volume	64
Issue number	1-2
DOIs	https://doi.org/10.1007/s12190-020-01374-z
State	Published - Oct 1 2020

Keywords

Code symmetries
Cyclic codes
Half-cyclic codes
Linear codes

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s12190-020-01374-z

Cite this

@article{74e05fbc2a324914a3563aa8e72a33aa,

title = "Half-cyclic, dihedral and half-dihedral codes",

abstract = "This note discusses, in elementary terms, linear codes over Z2 which are closed under 2-step cyclic shifts, and classifies them in terms of special linear combinations of polynomials. Codes which are preserved under order-reversing automorphisms are also discussed, and a classification result in terms of special linear combinations of polynomials is obtained.",

keywords = "Code symmetries, Cyclic codes, Half-cyclic codes, Linear codes",

author = "R. Jajcay and P. Poto{\v c}nik and S. Wilson",

note = "Publisher Copyright: {\textcopyright} 2020, Korean Society for Informatics and Computational Applied Mathematics.",

year = "2020",

month = oct,

day = "1",

doi = "10.1007/s12190-020-01374-z",

language = "English (US)",

volume = "64",

pages = "691--708",

journal = "Journal of Applied Mathematics and Computing",

issn = "1598-5865",

publisher = "Springer Nature",

number = "1-2",

}

TY - JOUR

T1 - Half-cyclic, dihedral and half-dihedral codes

AU - Jajcay, R.

AU - Potočnik, P.

AU - Wilson, S.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - This note discusses, in elementary terms, linear codes over Z2 which are closed under 2-step cyclic shifts, and classifies them in terms of special linear combinations of polynomials. Codes which are preserved under order-reversing automorphisms are also discussed, and a classification result in terms of special linear combinations of polynomials is obtained.

AB - This note discusses, in elementary terms, linear codes over Z2 which are closed under 2-step cyclic shifts, and classifies them in terms of special linear combinations of polynomials. Codes which are preserved under order-reversing automorphisms are also discussed, and a classification result in terms of special linear combinations of polynomials is obtained.

KW - Code symmetries

KW - Cyclic codes

KW - Half-cyclic codes

KW - Linear codes

UR - http://www.scopus.com/inward/record.url?scp=85086789688&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85086789688&partnerID=8YFLogxK

U2 - 10.1007/s12190-020-01374-z

DO - 10.1007/s12190-020-01374-z

M3 - Article

AN - SCOPUS:85086789688

SN - 1598-5865

VL - 64

SP - 691

EP - 708

JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

IS - 1-2

ER -

Half-cyclic, dihedral and half-dihedral codes

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this