A graph G with vertex set V is said to be n-existentially closed if, for every S ⊂ V with |S| = n and every T ⊆ S, there exists a vertex x ∈ V − S such that x is adjacent to each vertex of T but is adjacent to no vertex of S − T . Given a combinatorial design D with block set B, its block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and...

SHACAL-1 is an 80-round block cipher with a 160-bit block size and a key of up to 512 bits. In this paper, we present rectangle attacks on the first 51 rounds and a series of inner 52 rounds of SHACAL-1, and also present differential attacks on the first 49 rounds and a series of inner 55 rounds of SHACAL-1. These are the best currently known cryptanalytic results on SHACAL-1 in an one key atta...

Eukaryotic RNA polymerase III transcribes tRNA genes, and this requires the transcription factor TFIIIC. Promoters are within genes, with which the B-block binding subunit of TFIIIC associates to initiate transcription. The binding subunits are more than 1000 amino acids in length in various eukaryotic species. There are four regions with conserved sequence similarities in the subunits. The hel...

We investigate the existence of 3-designs and uniform large sets of 3-designs with block size 6 admitting PSL(2, q) as an automorphism group. We show the existence of simple 3-(28, 6, 10m) designs for 1 ≤ m ≤ 230. Most of these designs were previously unknown.

A structure for implementing lapped transforms with time-varying block sizes is presented which allows full orthogonality of the transient transforms. The formulation is based on a factorization of the transfer matrix into orthogonal factors. Such an approach can be viewed as a sequence of stages with variableblock-size transforms separated by sample-shu ing (delay) stages. Details and design e...

Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric bal...

An (v, •, 2) packing design of order v, block size ~, and index 2 is a collection of ~:-element subsets, called blocks, of a set V such that every 2-subsets of V occurs in at most 2 blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we provide a powerful technique for constructing designs and solve the packing problem in the case tc = 5, ...

We study three similar bijections on set partitions. The first gives a bijective proof of the equivalence of two statistics with a q-Stirling distribution, Milne’s statistic and the intertwining number. The second proves the equivalence of a multivariate block size distribution to a covering statistic. The third demonstrates equivalence of the number of all set partitions up to a given size to ...

Let V be a finite set of order v. A (V,K,A) packing design of index A and block size IC is a collection of K-element subsets, called blocks, such that every 2-subset of V occurs in at most A blocks. The packing problem is to determine the maximum number of blocks, D(V,K,A), in a packing design. It is well known that D(V,K,A) S [-i [:=~ ~]] : : t(VIK,~), where [xl is the largest integer satisfyi...

In this note the existence of a (Vj P2j 4, 2) BTD I for P2 = 0, 1 and 2, in which any pair of blocks intersect in at most two elements, is proved for any admissible v. A balanced ternary design is a collection of multi-sets of size k, chosen from a v-set in such a way that each element occurs 0, 1 or 2 times in anyone block, each pair of non-distinct elements, {x, x}, occurs in P2 blocks of the...