منابع مشابه
On the Nonexistence of Perfect Codes in the Johnson Scheme
Although it was conjectured by Delsarte in 1973 that no nontrivial perfect codes exist in the Johnson scheme, only very partial results are known. In this paper we considerably reduce the range in which perfect codes in the Johnson scheme can exist; e.g., we show that there are no nontrivial perfect codes in the Johnson graph J(2w qp, w), p prime. We give theorems about the structure of perfect...
متن کاملIntersection matrices and the Johnson scheme
In this paper we introduce a generating function F t sk(v)(z) which is a polynomial in terms of z whose coefficients are some intersection matrices. This provides a uniform framework in which several intersection matrices can be extracted from F t sk(v)(z). Several nice properties of F t sk(v)(z) are derived by applying the operator d/dz and studying the operator zd/dz. In the new framework som...
متن کاملOn Nonbinary 3-connected Matroids
It is well known that a matroid is binary if and only if it has no minor isomorphic to U2,4, the 4-point line. Extending this result, Bixby proved that every element in a nonbinary connected matroid is in a U2,4minor. The result was further extended by Seymour who showed that every pair of elements in a nonbinary 3-connected matroid is in a U2,4-minor. This paper extends Seymour's theorem by pr...
متن کاملConfiguration Distribution and Designs of Codes in the Johnson Scheme
The main goal of this article is to present several connections between perfect codes in the Johnson scheme and designs, and provide new tools for proving Delsarte conjecture that there are no nontrivial perfect codes in the Johnson scheme. Three topics will be considered. The first is the configuration distribution which is akin to the weight distribution in the Hamming scheme. We prove that i...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1985
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(85)80039-1