Paper Info
Title
Lower bounds for q-ary coverings by spheres of radius one
Abstract
Let C be a q -ary covering code with covering radius one. We give lower and upper bounds for the number of elements of C that lie in a fixed subspace of {0, …, q − 1} n . These inequalities lead to lower bounds for the cardinality of C that improve on the sphere covering bound. More precisely, we show that, if ( q − 1) n + 1 does not divide q n and if ( q , n ) ∉ {(2, 2), (2, 4)}, the sphere covering bound is never reached. This enables us to characterize the cases where the sphere covering bound is attained, when q is a prime power. We also present some improvements of the already known lower bounds for binary and ternary codes.
Year
DOI
Venue
1994
10.1016/0097-3165(94)90013-2
J. Comb. Theory, Ser. A
Keywords
Field
DocType
q-ary covering,lower bound
Discrete mathematics,Combinatorics,Covering code,Subspace topology,Cardinality,Ternary operation,SPHERES,Prime power,Mathematics,Binary number
Journal
Volume
Issue
ISSN
67
2
Journal of Combinatorial Theory, Series A
Citations 
PageRank 
References 
8
0.84
4
Authors
1
Name
Order
Citations
PageRank
Laurent Habsieger15813.44