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Type: Journal article
Title: (Re)constructing code loops
Author: Nagy, B.
Roberts, D.M.
Citation: American Mathematical Monthly, 2021; 128(2):151-161
Publisher: Taylor & Francis
Issue Date: 2021
ISSN: 0002-9890
Statement of
Ben Nagy and David Michael Roberts
Abstract: The Moufang loop named for Richard Parker is a central extension of the extended binary Golay code. It the prototypical example of a general class of nonassociative structures known today as code loops, which have been studied from a number of different algebraic and combinatorial perspectives. This expository article aims to highlight an experimental approach to computing in code loops, by a combination of a small amount of precomputed information and making use of the rich identities that code loops' twisted cocycles satisfy. As a byproduct we demonstrate that one can reconstruct the multiplication in Parker's loop from a mere fragment of its twisted cocycle. We also give relatively large subspaces of the Golay code over which Parker's loop splits as a direct product.
Description: Published online: 09 Feb 2021
Rights: © The Mathematical Association of America
DOI: 10.1080/00029890.2021.1852047
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Mathematical Sciences publications

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