Chapter

# Packing Arrays

DOI: 10.1007/3-540-45995-2_28
Source: DBLP

ABSTRACT

A packing array is a b×k array of values from a g-ary alphabet such that given any two columns, i and j, and for all ordered pairs of elements from the g-ary alphabet, (g1, g2), there is at most one row, r, such that ar,i = g1 and ar,j = g2. Further, there is a set of at least n rows that pairwise differ in each column: they are disjoint. A central question is to determine, for given g and k, the maximum possible b. We developg eneral direct and recursive constructions and upper bounds on the sizes of packing arrays. We also show the
equivalence of the problem to a matching problem on graphs and a class of resolvable pairwise balanced designs. We provide
tables of the best known upper and lower bounds.

### Full-text

Available from: Eric Mendelsohn, Aug 04, 2014
0 Followers
·
• ##### Article: Packing Arrays and Packing Designs
[Hide abstract]
ABSTRACT: A packing array is a b k array, A with entriesa i,j from a g-ary alphabet such that given any two columns,i and j, and for all ordered pairs of elements from a g-ary alphabet,(g 1, g 2), there is at most one row, r, such thata r,i = g 1 anda r,j = g 2. Further, there is a set of at leastn rows that pairwise differ in each column: they are disjoint. A central question is to determine, forgiven g, k and n, the maximum possible b. We examine the implications whenn is close to g. We give a brief analysis of the case n = g and showthat 2g rows is always achievable whenever more than g exist. We give an upper bound derivedfrom design packing numbers when n = g – 1. When g + 1 v < \frack(k - 1)2v < \frac{{k(k - 1)}}{2} .
Designs Codes and Cryptography 01/2002; 27(1):165-176. DOI:10.1023/A:1016567022721 · 0.96 Impact Factor
• Source
##### Article: Class-Uniformly Resolvable Group Divisible Structures I: Resolvable Group Divisible Designs
[Hide abstract]
ABSTRACT: We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction for shrinking the index of a master design. We construct a number of in nite families, primarily with block sizes 2 and k, including some extremal cases.
The electronic journal of combinatorics 04/2004; 11(1). · 0.49 Impact Factor
• Source
##### Article: On constant composition codes
[Hide abstract]
ABSTRACT: A constant composition code over a k-ary alphabet has the property that the numbers of occurrences of the k symbols within a codeword is the same for each codeword. These specialize to constant weight codes in the binary case, and permutation codes in the case that each symbol occurs exactly once. Constant composition codes arise in powerline communication and balanced scheduling, and are used in the construction of permutation codes. In this paper, direct and recursive methods are developed for the construction of constant composition codes.
Journal of Combinatorial Mathematics and Combinatorial Computing 04/2006; 154(6-154):912-929. DOI:10.1016/j.dam.2005.09.009