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Few-cosine spherical codes and Barnes–Wall lattices
- Source :
-
Journal of Combinatorial Theory - Series A . Oct2008, Vol. 115 Issue 7, p1211-1234. 24p. - Publication Year :
- 2008
-
Abstract
- Abstract: Using Barnes–Wall lattices and 1-cocycles on finite groups of monomial matrices, we give a procedure to construct tricosine spherical codes. This was inspired by a 14-dimensional code which Ballinger, Cohn, Giansiracusa and Morris discovered in studies of the universally optimal property. Their code has 64 vectors and cosines . We construct the Optimism Code, a 4-cosine spherical code with 256 unit vectors in 16-dimensions. The cosines are . Its automorphism group has shape . The Optimism Code contains a subcode related to the BCGM code. The Optimism Code implies existence of a nonlinear binary code with parameters , a Nordstrom–Robinson code, and gives a context for determining its automorphism group, which has form . [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 115
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 34253504
- Full Text :
- https://doi.org/10.1016/j.jcta.2008.02.001