A Steiner 2-design S(2,k,v) is said to be halvable if the block set can be partitioned into two isomorphic sets. This is equivalent to an edge-disjoint decomposition of a self-complementary graph G on v vertices into Kks. The obvious necessary condition of those orders v for which there exists a halvable S(2,k,v) is that v admits the existence of an S(2,k,v) with an even number of blocks. In th...

The paper proposes justification of using Mersenne primes in the following cryptoschemes: commutative and publickey encryption algorithms and zero-knowledge protocol. The cryptoschemes are based on computational difficulty of finding discrete logarithm in the finite fields GF (2), where s is a sufficiently large prime such that 2s−1 is also a prime, for example s = 1279, s = 2203, and s = 4253.

Let p be an odd prime. We first get some non-existence and structural results on (pn,p,pn,n) relative difference sets with gcd(p,n)= 1 through a group ring approach. We then give a construction of (p(p+ 1),p,p(p+ 1),p+ 1) relative difference sets with p a Mersenne prime.

We study orthogonal matrices whose elements have moduli ≤ 1. This paper shows that the existence of two such families of matrices is equivalent. Specifically we show that the existence of an Hadamard matrix of order 4t is equivalent to the existence of a 2-level Cretan-Mersenne matrix of order 4t − 1.

Personal MT (PMT) is a new concept in dialoguebased MT (DBMT) , which we are currently studying and prototyping in the LIDIA project Ideally, a PMT system should run on PCs and be usable by everybody. To get his/her text translated into one or several languages, the writer would accept to cooperate with the system in order to standardize and clarify his/her document. There are many interesting ...