Some 3-designs and a 4-design
نویسندگان
چکیده
منابع مشابه
Some New 4-Designs
The existence question for the family of 4-(15, 5, λ) designs has long been answered for all values of λ except λ = 2. Here, we resolve this last undecided case and prove that 4-(15, 5, 2) designs are constructible.
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Variations of the trade-off method exist in the literature of design theory and have been utilized by some authors to produce some t-designs with or without repeated blocks. In this paper we explore a new version of this algorithmic method (i) to produce 20 nonisomorphic and rigid 4-(12, 5, 4) designs, (ii) to study the spectrum of support sizes of 4-(12, 5, 4) designs. Along these, we also pre...
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The binary and ternary codes spanned by the rows of the point by block incidence matrices of some 2-designs and their complementary and orthogonal designs are studied. A new method is also introduced to study optimal codes.
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Automorphisms of Steiner 2-designs S(2, 4, 37) are studied and used to find many new examples. Some of the constructed designs have S(2, 3, 9) subdesigns, closing the last gap in the embedding spectrum of S(2, 3, 9) designs into S(2, 4, v) designs.
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In 1] Levenshtein and Vinck investigated perfect run{length{limited codes which are capable of correcting single peak shifts. As a basic combinatorial tool for the construction of such codes they introduced the concept of a t{shift N{design, which is deened to be an N{elementary subset H = fh 1 ; : : : h N g of a nite additive Abelian group G, with the property that for any = 1; : : : t and any...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1971
ISSN: 0097-3165
DOI: 10.1016/0097-3165(71)90045-8