منابع مشابه
Blocking sets in handcuffed designs
In this paper we determine the spectrum of possible cardinalities of a blocking set in a H(v,3,A) and in a H(v,4,1). Moreover we construct, for each admissible ~9, a H(v,3,1) without blocking sets. Introduction A handcuffed design with parameters v, k, A, or for short an H(v,k,A), consists of a set of ordered k-subsets of a v-set, called handcuffed blocks. In a block (a., a z ' ... ,a!:) each e...
متن کاملBlocking sets in balanced path designs
Let k ~ 3. For each admissible v, we determine the set BS1i ( v, k, 1) of integers x such that there exists a balanced path design H ( v, k, 1) with a blocking set of cardinality x.
متن کاملG-designs without blocking sets, Note
For an undirected graph G and a natural number n, a G-design of order n is an edge partition of the complete graph Kn with n vertices into subgraphs G1, G2, . . . , each isomorphic to G. A set T ⊂ V (Kn) is called a blocking set if it meets the vertex set V (Gi) of each Gi in the decomposition, but contains none of them. In a previous paper [J. Combin. Designs 4 (1996), 135–142] the first and t...
متن کاملHigh-rate LDPC codes from unital designs
This paper presents a construction of very high-rate low-density parity-check (LDPC) codes based on the incidence matrices of unital designs. Like the projective geometry and oval designs, unital designs exist with incidence matrices which are significantly rank deficient. Thus high-rate LDPC codes with a large number of linearly dependent parity-check equations can be constructed. The LDPC cod...
متن کاملBlocking Sets in (v, {2, 4}, 1)-Designs
The existence of blocking sets in (v, {2, 4}, 1)-designs is examined. We show that for v ≡ 0, 3, 5, 6, 7, 8, 9, 11 (mod 12), blocking sets cannot exist. We prove that for each v ≡ 1, 2, 4 (mod 12) there is a (v, {2, 4}, 1)-design with a blocking set with three possible exceptions. The case v ≡ 10 (mod 12) is still open; we consider the first four values of v in this situation.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.02.023