A Partition of the Hypercube into Maximally Nonparallel Hamming Codes

By using the Gold map, we construct a partition of the hypercube into cosets of Hamming codes such that for every two cosets the corresponding Hamming codes are maximally nonparallel, that is, their intersection cardinality is as small as possible to admit nonintersecting cosets.

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Bibliographic Details
Published inJournal of combinatorial designs Vol. 22; no. 4; pp. 179 - 187
Main Author Krotov, Denis S.
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.04.2014
Wiley Subscription Services, Inc
Subjects
1-perfect partition
crooked permutation
Gold function
Hamming codes
perfect code
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Summary:By using the Gold map, we construct a partition of the hypercube into cosets of Hamming codes such that for every two cosets the corresponding Hamming codes are maximally nonparallel, that is, their intersection cardinality is as small as possible to admit nonintersecting cosets.
Bibliography:Target program of SB RAS - No. 2012-2014
RFBR - No. 13-01-00463
ark:/67375/WNG-VN896MZH-H
ArticleID:JCD21363
Ministry of education and science of Russian Federation - No. 8227
istex:F710A7AA99884174D2B72203F5D49C7D332F7300
Contract grant sponsor: RFBR; contract grant number: 13‐01‐00463.
ISSN:1063-8539
1520-6610
DOI:10.1002/jcd.21363