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Ranks of incidence matrices of Steiner triple systems

✍ Scribed by Jean Doyen; Xavier Hubaut; Monique Vandensavel

Book ID: 105105590
Publisher: Springer-Verlag
Year: 1978
Tongue: French
Weight: 498 KB
Volume: 163
Category: Article
ISSN: 0025-5874
DOI: 10.1007/bf01174898

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📜 SIMILAR VOLUMES

Embeddings of Steiner triple systems

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If X is a set whose elements are called points and A is a collectioxr of subsets of X (called lines) such that: (i) any two distinct points of X are contained in exactly one line, (ii) every line contains at least two points, we say that the pair (X, A) is a linear space. A Steiner triple system i

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A Steiner triple system of order n (STS(n)) is said to be embeddable in an orientable surface if there is an orientable embedding of the complete graph Kn whose faces can be properly 2-colored (say, black and white) in such a way that all black faces are triangles and these are precisely the blocks

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The code over a finite field F, of a design D is the space spanned by the incidence vectors of the blocks. It is shown here that if D is a Steiner triple system on v points, and if the integer then the ternary code C of contains a subcode that can be shortened to the ternary generalized Reed-Muller

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✍ Peter Dukes; Eric Mendelsohn 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB

## Abstract In this paper, we present a conjecture that is a common generalization of the Doyen–Wilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given __u__, __v__ ≡ 1,3 (mod 6), __u__ < __v__ < 2__u__ + 1, we ask for the minimum __r__ such that there exists a