# New Upper Bounds for Some Spherical Codes

Boyvalenkov, Peter; Kazakov, Peter

Serdica Mathematical Journal (1995)

- Volume: 21, Issue: 3, page 231-238
- ISSN: 1310-6600

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topBoyvalenkov, 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 -

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