A group ring construction of the extended binary Golay code

Ian McLoughlin; Ted Hurley

doi:10.1109/TIT.2008.928260

A group ring construction of the extended binary Golay code

Ian McLoughlin
, Ted Hurley

Mathematics

University of Galway

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

27 Citations (Scopus)

Abstract

We give a new construction of the extended binary Golay code. The code is constructed as a zero divisor code over the dihedral group of twenty-four elements, D₂₄. The construction is algebraic, much like the construction of the (23,12,7) binary Golay code from a polynomial.

Original language	English
Pages (from-to)	4381-4383
Number of pages	3
Journal	IEEE Transactions on Information Theory
Volume	54
Issue number	9
DOIs	https://doi.org/10.1109/TIT.2008.928260
Publication status	Published - 2008

Keywords

Block codes
Dual codes
Golay codes
Group theory
Rings (algebraic)

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10.1109/TIT.2008.928260

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title = "A group ring construction of the extended binary Golay code",

abstract = "We give a new construction of the extended binary Golay code. The code is constructed as a zero divisor code over the dihedral group of twenty-four elements, D24. The construction is algebraic, much like the construction of the (23,12,7) binary Golay code from a polynomial.",

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AU - Hurley, Ted

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AB - We give a new construction of the extended binary Golay code. The code is constructed as a zero divisor code over the dihedral group of twenty-four elements, D24. The construction is algebraic, much like the construction of the (23,12,7) binary Golay code from a polynomial.

KW - Block codes

KW - Dual codes

KW - Golay codes

KW - Group theory

KW - Rings (algebraic)

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U2 - 10.1109/TIT.2008.928260

DO - 10.1109/TIT.2008.928260

M3 - Article

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SP - 4381

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JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 9

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A group ring construction of the extended binary Golay code

Abstract

Keywords

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