A doubly resolvable packing design with block size k, index lambda, replication number r, and nu elements is called a generalized Kirkman square and denoted by GKS(k) (nu;1, lambda;r). Existence of GKS(3) (4u;1, 1;2(u...
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A doubly resolvable packing design with block size k, index lambda, replication number r, and nu elements is called a generalized Kirkman square and denoted by GKS(k) (nu;1, lambda;r). Existence of GKS(3) (4u;1, 1;2(u - 1))s and GKS(3)(6u;1, 1;3(u - 1))s is implied by existence of doubly resolvable group divisible designs with block size 3, index 1, and types 4(u) and 6(u) (i.e., (3, 1)-DRGDDs of types 4(u) and 6(u). In this paper, we establish the spectra of (3, 1)-DRGDDs of types 4(u) and 6(u) with 15 and 31 possible exceptions, respectively. As applications, we get some new classes of permutation codes and doubly constant weight codes. We also construct 5 new resolvable GDDs with block size 4 and index 1. (C) 2015 Elsevier B.V. All rights reserved.
A doubly constant weight code is a binary code of length n(1) + n(2), with constantweight w(1) + w(2), such that the weight of a codeword in the first n(1) coordinates is w(1). Such codes have applications in obtaini...
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A doubly constant weight code is a binary code of length n(1) + n(2), with constantweight w(1) + w(2), such that the weight of a codeword in the first n(1) coordinates is w(1). Such codes have applications in obtaining bounds on the sizes of constantweightcodes with given minimum distance. Lower and upper bounds on the sizes of such codes are derived. In particular, we show tight connections between optimal codes and some known designs such as Howell designs, Kirkman squares, orthogonal arrays, Steiner systems, and large sets of Steiner systems. These optimal codes are natural generalization of Steiner systems and they are also called doubly Steiner systems. (C) 2007 Wiley Periodicals, Inc.
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