On spherical codes with inner products in a prescribed interval

被引：5

作者：

Boyvalenkov, P. G. ^{[1
,2
]}

Dragnev, P. D. ^{[3
]}

Hardin, D. P. ^{[4
]}

Saff, E. B. ^{[4
]}

Stoyanova, M. M. ^{[5
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, 8 G Bonchev Str, BU-1113 Sofia, Bulgaria

[2] South Western Univ, Blagoevgrad, Bulgaria

[3] Purdue Univ, Dept Math Sci, Ft Wayne, IN 46805 USA

[4] Vanderbilt Univ, Dept Math, Ctr Construct Approximat, Nashville, TN 37240 USA

[5] Sofia Univ, Fac Math & Informat, 5 James Bourchier Blvd, Sofia 1164, Bulgaria

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2019年 / 87卷 / 2-3期

基金：

美国国家科学基金会;

关键词：

Spherical codes; Linear programming; Bounds for codes; H-energy of a code; ENERGY; BOUNDS;

D O I：

10.1007/s10623-018-0524-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval [,s] of [-1,1). An intricate relationship between Levenshtein-type upper bounds on cardinality of codes with inner products in [,s] and lower bounds on the potential energy (for absolutely monotone interactions) for codes with inner products in [,1) (when the cardinality of the code is kept fixed) is revealed and explained. Thereby, we obtain a new extension of Levenshtein bounds for such codes. The universality of our bounds is exhibited by a unified derivation and their validity for a wide range of codes and potential functions.

引用

页码：299 / 315

页数：17

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