62,662 research outputs found
Estimates on the Size of Symbol Weight Codes
The study of codes for powerlines communication has garnered much interest
over the past decade. Various types of codes such as permutation codes,
frequency permutation arrays, and constant composition codes have been proposed
over the years. In this work we study a type of code called the bounded symbol
weight codes which was first introduced by Versfeld et al. in 2005, and a
related family of codes that we term constant symbol weight codes. We provide
new upper and lower bounds on the size of bounded symbol weight and constant
symbol weight codes. We also give direct and recursive constructions of codes
for certain parameters.Comment: 14 pages, 4 figure
Constructions of Optimal and Near-Optimal Multiply Constant-Weight Codes
Multiply constant-weight codes (MCWCs) have been recently studied to improve
the reliability of certain physically unclonable function response. In this
paper, we give combinatorial constructions for MCWCs which yield several new
infinite families of optimal MCWCs. Furthermore, we demonstrate that the
Johnson type upper bounds of MCWCs are asymptotically tight for fixed weights
and distances. Finally, we provide bounds and constructions of two dimensional
MCWCs
New Upper Bounds on Codes via Association Schemes and Linear Programming
Let A(n, d) denote the maximum number of codewords in a binary code of length n and minimum Hamming distance d. Upper and lower bounds on A(n, d) have been a subject for extensive research. In this paper we examine upper bounds on A(n, d) as a special case of bounds on the size of subsets in metric association scheme. We will first obtain general bounds on the size of such subsets, apply these bounds to the binary Hamming scheme, and use linear programming to further improve the bounds. We show that the sphere packing bound and the Johnson bound as well as other bounds are special cases of one of the bounds obtained from association schemes. Specific bounds on A(n, d) as well as on the sizes of constant weight codes are also discussed
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