A design and a code invariant under the simple group Co3

Willem H. Haemers; Christopher Parker; Vera Pless; Vladimir D. Tonchev

doi:10.1016/0097-3165(93)90045-A

A design and a code invariant under the simple group Co₃

Willem H. Haemers^*, Christopher Parker, Vera Pless, Vladimir D. Tonchev

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A self-orthogonal doubly-even (276, 23) code invariant under Conway’s simple group Co₃ is constructed. The minimum weight codewords form a 2-(276, 100, 1458) doubly transitive block-primitive design with block stabilizer isomorphic to the Higman-Sims simple group HS. More generally, the codewords of any given weight are single orbits stabilized by maximal subgroups of Co₃. The restriction of the code on the complement of a minimum weight codeword is the (176, 22) code discovered by Calderbank and Wales as a code invariant under HS.

Original language	English
Pages (from-to)	225-233
Number of pages	9
Journal	Journal of Combinatorial Theory, Series A
Volume	62
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(93)90045-A
Publication status	Published - 1993

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1016/0097-3165(93)90045-A

Cite this

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abstract = "A self-orthogonal doubly-even (276, 23) code invariant under Conway{\textquoteright}s simple group Co3 is constructed. The minimum weight codewords form a 2-(276, 100, 1458) doubly transitive block-primitive design with block stabilizer isomorphic to the Higman-Sims simple group HS. More generally, the codewords of any given weight are single orbits stabilized by maximal subgroups of Co3. The restriction of the code on the complement of a minimum weight codeword is the (176, 22) code discovered by Calderbank and Wales as a code invariant under HS.",

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AU - Parker, Christopher

AU - Pless, Vera

AU - Tonchev, Vladimir D.

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N2 - A self-orthogonal doubly-even (276, 23) code invariant under Conway’s simple group Co3 is constructed. The minimum weight codewords form a 2-(276, 100, 1458) doubly transitive block-primitive design with block stabilizer isomorphic to the Higman-Sims simple group HS. More generally, the codewords of any given weight are single orbits stabilized by maximal subgroups of Co3. The restriction of the code on the complement of a minimum weight codeword is the (176, 22) code discovered by Calderbank and Wales as a code invariant under HS.

AB - A self-orthogonal doubly-even (276, 23) code invariant under Conway’s simple group Co3 is constructed. The minimum weight codewords form a 2-(276, 100, 1458) doubly transitive block-primitive design with block stabilizer isomorphic to the Higman-Sims simple group HS. More generally, the codewords of any given weight are single orbits stabilized by maximal subgroups of Co3. The restriction of the code on the complement of a minimum weight codeword is the (176, 22) code discovered by Calderbank and Wales as a code invariant under HS.

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