Covering all triples on n marks by disjoint Steiner systems
TL;DR: Let q be a number all whose prime factors divide integers of the form 2s − 1, s odd, if n = q + 2, the (3n) triples on n marks can be partitioned into q sets, each forming a Steiner triple system.
About: This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-11-01 and is currently open access. It has received 39 citations till now. The article focuses on the topics: Steiner system & Disjoint sets.
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TL;DR: The known techniques for constructing constant weight codes are surveyed, and a table of (unrestricted) binary codes of length nl28 is given.
Abstract: A table of binary constant weight codes of length nl28 is presented. Explicit constructions are given for most of the 600 codes in the table; the majority of these codes are new. The known techniques for constructing constant weight codes are surveyed, and a table of (unrestricted) binary codes of length nl28 is given
459 citations
TL;DR: In this paper, a disjoint Latin square of order n with n parallel transversals including the diagonal one is constructed, which is called LDS(n) and is a set of n + 2 pairwise disjunctional Latin squares.
140 citations
TL;DR: A Steiner system S( t, k, O) is a pair (S, B) where S is a u-set and B is a collection of k-subsets of S such that every t-subset of S is contained in exactly one member of B.
119 citations
TL;DR: The role of combinatorial designs in solving many problems that are basic to the field of computing is explored and paradigms in which designs can be used profitably in algorithm design and analysis are suggested.
Abstract: The theory of combinatorial designs has been used in widely different areas of computation concerned with the design and analysis of both algorithms and hardware. Combinatorial designs capture a subtle balancing property that is inherent in many difficult problems and hence can provide a sophisticated tool for addressing these problems. The role of combinatorial designs in solving many problems that are basic to the field of computing is explored in this paper. Case studies of many applications of designs to computation are given; these constitute a first survey, which provides a representative sample of uses of designs. More importantly, they suggest paradigms in which designs can be used profitably in algorithm design and analysis.
64 citations
Cites methods from "Covering all triples on n marks by ..."
...For p a prime congruent to 7 modulo 8, optimal (3, 3, p + 2)-threshold schemes can be constructed by using a partition due to Schreiber [1973] and Wilson [1974] of a 3 - (p + 2, 3, 1) design into p 2 - (p + 2,...
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TL;DR: A new proof of the existence of an LSTS(v) for any v ≡ 1 or 3 (mod 6) with six possible exceptions and a definite exception v = 7 is given.
49 citations
Cites background from "Covering all triples on n marks by ..."
...Besides, Schreiber (1973) [24], Wilson [28] and Denniston (1974) [3] successively got some small orders....
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01 Feb 1972
TL;DR: In this paper, a lower bound for the maximum number of pairwise disjoint and isomorphic Steiner triple systems of order v is given, namely D*(6r+3)^ 4t-1 or 4/1 according as 2/1 is or is not divisible by 3, and D*6f+l)^?/2 or t according as t is even or odd.
Abstract: Let D*(v) denote the maximum number of pairwise disjoint and isomorphic Steiner triple systems of order v. The main result of this paper is a lower bound for D*(v), namely D*(6r+3)^ 4t—1 or 4/+1 according as 2/+1 is or is not divisible by 3, and D*(6f+l)^?/2 or t according as t is even or odd. Some other related problems are studied or proposed for study. © 1972 American Mathematical Society.
60 citations