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

页码：6898 / 6907

页数：10

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