Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/129988
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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 1930-0972 |
Statement of Responsibility: | 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 |
Grant ID: | http://purl.org/au-research/grants/arc/DP180100383 |
Published version: | http://dx.doi.org/10.1080/00029890.2021.1852047 |
Appears in Collections: | Aurora harvest 8 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
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hdl_129988.pdf | Submitted version | 875.74 kB | Adobe PDF | View/Open |
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