✦ LIBER ✦

On the extendability of steiner t-designs

✍ Scribed by Alphonse H. Baartmans; Ian F. Blake; Vladimir D. Tonchev

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 448 KB
Volume: 1
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180010305

No coin nor oath required. For personal study only.

✦ Synopsis

Necessary and sufficient conditions for the extendability of residual designs of Steiner systems S ( t , t + 1, v) are studied. In particular, it is shown that a residual design with respect to a single point is uniquely extendable, and the extendability of a residual design with respect to a pair of points is equivalent to a bipartition of the block graph of a related design.

📜 SIMILAR VOLUMES

On Steiner 3-wise balanced designs of or

On Steiner 3-wise balanced designs of order 17

✍ E. S. Kramer; D. L. Kreher; Rudolf Mathon 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 231 KB

We determine all S(3, K, 17)'s which either; (i) have a block of size at least 6; or (ii) have an automorphism group order divisible by 17, 5, or 3; or (iii) contain a semi-biplane; or (iv) come from an S(3, K, 16) which is not an S(3, 4, 16). There is an S(3, K, 17) with |G| = n if and only if n ∈

On the Extendability of Linear Codes

✍ Tatsuya Maruta 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 237 KB

Symposium on Inform. Theory, Whistler, Canada,'' pp. 345) proved that every [n, k, d] O code with gcd(d, q)"1 and with all weights congruent to 0 or d (modulo q) is extendable to an O code with all weights congruent to 0 or d#1 (modulo q). We give another elementary geometrical proof of this theor

On the 2-extendability of the generalize

On the 2-extendability of the generalized Petersen graphs

✍ Gerald Schrag; Larry Cammack 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 731 KB

A graph G is n-extendable if it is connected, contains a set of rr independent edges and every set of n-independent edges extends to (i.e. is a subset of) a perfect matching. Combining the results of this and previous papers we answer the question of 2-extendability for all the generalized Petersen

Some results on the existence of large s

Some results on the existence of large sets of t-designs

✍ G. B. Khosrovshahi; R. Tayfeh-Rezaie 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 96 KB 👁 1 views

## Abstract A set of trivial necessary conditions for the existence of a large set of __t__‐designs, __LS__[N](__t,k,__ν), is $N\big | {{\nu \hskip -3.1 \nu}-i \choose k-i}$ for __i__ = 0,…,__t__. There are two conjectures due to Hartman and Khosrovshahi which state that the trivial necessary condi

On the number of partial Steiner systems

✍ A. S. Asratian; N. N. Kuzjurin 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 101 KB 👁 2 views

On the amicability of orthogonal designs

✍ W. H. Holzmann; H. Kharaghani 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB

## Abstract Although it is known that the maximum number of variables in two amicable orthogonal designs of order 2^__n__^__p__, where __p__ is an odd integer, never exceeds 2__n__+2, not much is known about the existence of amicable orthogonal designs lacking zero entries that have 2__n__+2 variab