Record number :

1600212

Title of article :

Covering codes and extremal problems from invariant sets under permutations

Author/Authors :

Carmelo، نويسنده , , Emerson L. Monte Carmelo، نويسنده ,

Issue Information :

روزنامه با شماره پیاپی سال 2013

Pages :

9

From page :

249

To page :

257

Abstract :

Let c q ( n , R ) denote the minimum cardinality of a subset H in F q n such that every word in this space differs in at most R coordinates from a scalar multiple of a vector in H , where q is a prime power. In order to explore symmetries of such coverings, a few properties of invariant sets under certain permutations are investigated. New classes of upper bounds on c q ( n , R ) are obtained, extending previous results. Let K q ( n , R ) denote the minimum cardinality of an R -covering code in the n -dimensional space over an alphabet with q symbols. As another application, a very-known upper bound on K q ( n , R ) is improved under certain conditions. Moreover, two extremal problems are discussed by using tools from graph theory.

Keywords :

Permutation , Covering , Invariant set , Independent set , Matching , Bounds on code

Journal title :

Discrete Mathematics

Serial Year :

2013

Link To Document :