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Studia Scientiarum Mathematicarum Hungarica
Author:
Jörn Quistorff
Let
n, k
∈ ℕ with 2
k
≦
n
and
X
be an
n
-set. The Enomoto-Katona space \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{upgreek}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\usepackage{bbm}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\mathcal{R}: = \left\{ {\{ A,B\} \subseteqq \left( {_k^X } \right)\left| {A \cap } \right.B = \not 0} \right\},$$
\end{document} consisting of all unordered pairs of disjoint
k
-element subsets of
X
and equipped with \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{upgreek}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\usepackage{bbm}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$d^\mathcal{R}$$
\end{document} ({
A,B
}, {
S,T
}) ≔ min {|
A
\
S
|+|
B
\
T
|,|
A
\
T
|+|
B
\
S
|}, is considered. The proof of the triangle inequality for \documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{upgreek}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\usepackage{bbm}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$d^\mathcal{R}$$
\end{document} is simplified. Upper bounds on the coding type problem, i.e. the determination of the maximum cardinality of a code consisting of unordered pairs of subsets far away from each other, are improved. The sphere packing problem, i.e. the determination of the maximum number of disjoint balls of a prescribed radius, is introduced and discussed. It is less closely connected to the first problem than it is in the most important spaces of coding theory.
Studia Scientiarum Mathematicarum Hungarica
Authors:
Jörn Quistorff
and
Jan-Christoph Schlage-Puchta
We consider generalized surjective codes, together with their connection to covering codes and covering arrays. We prove new bounds on σ q(n; s; r), the minimal cardinality of a q-ary code of length n, which is s-surjective with radius r. For covering codes we deduce the new records K 6(10, 7) ≦ 18 and K 6(9, 6) ≦ 24.
