Transmission over Multiple Input Multiple Output (MIMO) radio channels is considered. When multiple Rx antennas are present, one may simultaneously increase the rate and improve performance by optimizing transmit diversity, using nonorthogonal space-time block codes. This improves the performance of MIMO systems considerably, especially when the number of Tx and Rx antennas is small. As an exam...

Let G be the projective special linear group PSL(2, 2), let X be the projective line and B be any subgroup of GF ∗(2n). We give a new infinite family of simple 3-designs by determining the parameter set of (X, G(B0)), where B0 = B ∪ {0}.

We find a natural construction of a large class of symmetric graphs from pointand block-transitive 1-designs. The graphs in this class can be characterized as G-symmetric graphs whose vertex sets admit a G-invariant partition B of block size at least 3 such that, for any two blocks B,C of B, either there is no edge between B and C , or there exists only one vertex in B not adjacent to any verte...

A Mendelsohn design .M D(v, k,).) is a pair (X, B), where X is a vset together with a collection B of ordered k-tuples from X such that each ordered pair from X is contained in exactly ). k-tuples of B. An M D(v, k,).) is said to be self-converse, denoted by SC!'vf D( v, k,).) = (X,B,/), if there is an isomorphism / from (X, B) to (X,B), where B-1 {(Xk,:r:k-l, ... ,X2,Xl); (Xl,,,,,Xk) E B}. The...

A necessary condition is given for the existence of some Generalised Bhaskar Rao designs (GBRDs) with odd block size over cyclic groups of even order. Some constructions are given for GBRDs over cyclic groups of even order with block size 3 and with block size 4. AMS Subject Classification: 05B99 J( ey words and phrases: Balanced Incomplete Block Designs; Generalised Bhaskar Rao Designs

Alspach, B. and D. Hare, Edge-pancyclic block-intersection graphs, Discrete Mathematics 97 (1991) 17-24. It is shown that the block-intersection graph of both a balanced incomplete block design with block size at least 3 and A = 1, and a transversal design is edge-pancyclic.

The group PSL(2, q) is 3-homogeneous on the projective line when q is a prime power congruent to 3 modulo 4 and therefore it can be used to construct 3-designs. In this paper, we determine all 3-designs admitting PSL(2, q) with block size not congruent to 0 and 1 modulo p where q = pn.

Well-known necessary conditions for the existence of a generalized Bhaskar Rao design, GBRD(v, 3, λ;G) with v ≥ 4 are: (i) λ ≡ 0 (mod |G|), (ii) λ(v − 1) ≡ 0 (mod 2), (iii) λv(v − 1) ≡ 0 (mod 3), (iv ) if |G| ≡ 0 (mod 2) then λv(v − 1) ≡ 0 (mod 8). In this paper we show that these conditions are sufficient whenever (i) the group G has odd order or (ii) the order is of the form 2q for q = 3 or q...

Let (W, C) be an m-cycle system of order n and let Ω ⊂ W , |Ω| = v < n. We say that a path design (Ω,P) of order v and block size s (2 ≤ s ≤ m− 1) is embedded in (W, C) if for every p ∈ P there is an m-cycle c = (a1, a2, . . . , am) ∈ C such that: (1) p = [ak, ak+1, . . . , ak+s−1] for some k ∈ {1, 2, . . . ,m} (i.e. the (s− 1)-path p occurs in the m-cycle c); and (2) ak−1, ak+s ∈ Ω. Note that ...

A (v, K, A) packing design of order v, block size K, and index 1 is a collection of K-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most L blocks. The packing problem is to determine the maximum number of blocks in a packing design. Packing with 1= 2 is called bipacking. In this paper we solve the bipacking problem in the case K = 5 and v = 13 (mod 20).