A (u, K, 1) packing design of order o, block size K, and index I is a collection of K-element subsets, called blocks of a set V such that every 2-subset of V occurs in at most 1 blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we solve the packing problem with K = 5, 1=8, 12, 16, and all positive integers o with the possible exceptions ...

A balanced ternary design of order v with block size three, index 2 and P2 = 1 is a collection of multi-subsets of size 3 (of type { x, y, z} or {x, x, y }) called blocks, in which each unordered pair of distinct elements occurs twice possibly in one block and in which each element is repeated in just one block. So there are precisely v blocks of type {x, x, y}. Necessarily v == 0 (mod 3). We d...

The IEEE 802.16 standard defines the ARQ mechanism as a part of the MAC layer. The functioning of the ARQ mechanism depends on a number of parameters. The IEEE 802.16 specification defines them but it does not provide concrete values and solutions. This paper studies the key features and parameters of the 802.16 ARQ mechanism. In particular, we consider a choice for the ARQ feedback type, an al...

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...

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, ...