On the Algebraic Combinatorics of Injections and its Applications to Injection Codes

被引：3
|
作者：
Dukes, Peter J. [1 ]
Ihringer, Ferdinand [2 ]
Lindzey, Nathan [3 ]
机构：
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8P 5C2, Canada
[2] Univ Ghent, Dept Math Anal Log & Discrete Math, B-9000 Ghent, Belgium
[3] Univ Colorado, Dept Comp Sci, Boulder, CO 80309 USA
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2020年 / 66卷 / 11期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Standards; Shape; Strips; Hamming distance; Linear programming; Eigenvalues and eigenfunctions; Indexes; Permutation code; linear programming bound; injection; partial permutation; representation theory; association scheme; PERMUTATION; BOUNDS;
D O I：
10.1109/TIT.2020.3005544
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We consider the algebraic combinatorics of the set of injections from a k-element set to an n-element set. In particular, we give a new combinatorial formula for the spherical functions of the Gelfand pair (S-k x S-n, diag(S-k) x Sn- k). We use this combinatorial formula to give new Delsarte linear programming bounds on the size of codes over injections.
引用
收藏
页码：6898 / 6907
页数：10
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