New Upper Bounds for Some Spherical Codes

Boyvalenkov, Peter, and Kazakov, Peter. "New Upper Bounds for Some Spherical Codes." Serdica Mathematical Journal 21.3 (1995): 231-238. <http://eudml.org/doc/11669>.

@article{Boyvalenkov1995,
abstract = {The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.},
author = {Boyvalenkov, Peter, Kazakov, Peter},
journal = {Serdica Mathematical Journal},
keywords = {Spherical Codes; Linear Programming Bounds; Distance Distribution; upper bounds; linear programming bounds; Levenshtein bounds},
language = {eng},
number = {3},
pages = {231-238},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {New Upper Bounds for Some Spherical Codes},
url = {http://eudml.org/doc/11669},
volume = {21},
year = {1995},
}

TY - JOUR
AU - Boyvalenkov, Peter
AU - Kazakov, Peter
TI - New Upper Bounds for Some Spherical Codes
JO - Serdica Mathematical Journal
PY - 1995
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 21
IS - 3
SP - 231
EP - 238
AB - The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.
LA - eng
KW - Spherical Codes; Linear Programming Bounds; Distance Distribution; upper bounds; linear programming bounds; Levenshtein bounds
UR - http://eudml.org/doc/11669
ER -