scholarly journals Bounds for the Minimum Distance and Covering Radius of Orthogonal Arrays via Their Distance Distributions

2021 ◽  
Author(s):  
Silvia Boumova ◽  
Peter Boyvalenkov ◽  
Maya Stoyanova
Keyword(s):  
Minimum Distance ◽  
Orthogonal Arrays ◽  
Analytic Form ◽  
Covering Radius ◽  
Distance Distributions ◽  
Feasible Sets ◽  
Ongoing Project

We propose two methods for obtaining estimations on the minimum distance and covering radius of orthogonal arrays. Both methods are based on knowledge about the (feasible) sets of distance distributions of orthogonal arrays with given length, cardinality, factors and strength. New bounds are presented either in analytic form and as products of an ongoing project for computation and investigation of the possible distance distributions of orthogonal arrays with parameters in doable ranges.

New Results on Codes with Covering Radius 1 and Minimum Distance 2

2005 ◽  
Vol 35 (2) ◽  
pp. 241-250 ◽  
Author(s):  
Patric R. J. �sterg�rd ◽  
J�rn Quistorff ◽  
Alfred Wassermann
Keyword(s):  
Minimum Distance ◽  
Covering Radius

scholarly journals On Mixed Codes with Covering Radius $1$ and Minimum Distance $2$

10.37236/969 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Wolfgang Haas ◽  
Jörn Quistorff
Keyword(s):  
Lower Bounds ◽  
Minimum Distance ◽  
Covering Radius ◽  
Minimal Cardinality ◽  
Finite Sets ◽  
Open Problems ◽  
Latin Rectangle ◽  
Mixed Codes ◽  
Special Case

Let $R$, $S$ and $T$ be finite sets with $|R|=r$, $|S|=s$ and $|T|=t$. A code $C\subset R\times S\times T$ with covering radius $1$ and minimum distance $2$ is closely connected to a certain generalized partial Latin rectangle. We present various constructions of such codes and some lower bounds on their minimal cardinality $K(r,s,t;2)$. These bounds turn out to be best possible in many instances. Focussing on the special case $t=s$ we determine $K(r,s,s;2)$ when $r$ divides $s$, when $r=s-1$, when $s$ is large, relative to $r$, when $r$ is large, relative to $s$, as well as $K(3r,2r,2r;2)$. Some open problems are posed. Finally, a table with bounds on $K(r,s,s;2)$ is given.

The covering radius of the Leech lattice

1982 ◽  
Vol 380 (1779) ◽  
pp. 261-290 ◽  
Keyword(s):  
Minimum Distance ◽  
Dimensional Space ◽  
Covering Radius ◽  
Lattice Points ◽  
Maximum Distance ◽  
Leech Lattice

We investigate the points in 24-dimensional space at maximum distance from the Leech lattice, i. e. the ‘deepest holes’ in that lattice. The maximum distance of any such point from the Leech lattice is shown to be 1/√2 times the minimum distance between the lattice points. Furthermore there are 23 types of ‘deepest hole’, one for each of the 23 even unimodular 24-dimensional lattices found by Niemeier.

Nonexistence of binary orthogonal arrays via their distance distributions

2015 ◽  
Vol 51 (4) ◽  
pp. 326-334 ◽  
Author(s):  
P. Boyvalenkov ◽  
H. Kulina ◽  
T. Marinova ◽  
M. Stoyanova
Keyword(s):  
Orthogonal Arrays ◽  
Distance Distributions
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