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

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10.1007/s12190-020-01374-z

Cite this

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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.",

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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.

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KW - Cyclic codes

KW - Half-cyclic codes

KW - Linear codes

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Half-cyclic, dihedral and half-dihedral codes

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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