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

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A new table of constant weight codes

On large sets of disjoint steiner triple systems, IV

Steiner quadruple systems - a survey

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.

/pdf/applications-of-combinatorial-designs-in-computer-science-6u2m2654ra.pdf

Applications of combinatorial designs in computer science

Locally trivial t -designs and t -designs without repeated blocks

Covering all triples on n marks by disjoint Steiner systems

Letq=6t±1, ν=2q+2. The (ν/3) tri ples on ν marks may be partitioned intoq sets, each forming a BIBD of parameters (ν,3,2). Related results, some of them known, are also discussed briefly.

Some balanced complete block designs

For the rational integera and the rational primeb, letP(a,b) be the set of primesp such that\(\left( i \right) \left( {p,a\left( {a - 1} \right)} \right) = 1,b|\left( {p - 1} \right)\left( {\exists c \in N,bcX,p|\frac{{a^{bc} - 1}}{{a^c - 1}}} \right)\). A natural integerq satisfies (i) iffq is a power product fromP(a,b). In the (additively written) Abelian groupG, g→ag permutes the elements ofG# in cycles whose lengths are multiples ofb, but not ofb2, iffG is aπ-group withπ⊂P (a,b). The casea=−2,b=2 has combinational applications.

Shmuel Schreiber

Papers

Covering all triples on n marks by disjoint Steiner systems

Some balanced complete block designs

Some mappings of pfriodic groups