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
收藏
页码：299 / 315
页数：17
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