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arXiv · 1903.02748

(Re)constructing Code Loops

Ben Nagy·David Michael Roberts
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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.

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Ben Nagy, David Michael Roberts. 2019-03-07. (Re)constructing Code Loops. https://doi.org/10.1080/00029890.2021.1852047

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