We introduce space–time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space–time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbe...

It is proved that the collection of blocks of an affine 1-design that yields a linear orthogonal array is a union of parallel classes of hyperplanes in a finite affine space. In particular, for every prime power q and every m ≥ 2 there exists a unique (up to equivalence) complete linear orthogonal array of strength two associated with the classical design of points and hyperplanes in AG(m, q).

Given any -tuple ( s1, s2, . . . , s ) of positive integers, there is an integer N = N ( s1, s2, . . . , s ) such that an orthogonal design of order 2 ( s1 + s2 + · · ·+ s ) and type ( 2s1, 2 s2, . . . , 2 s ) exists, for each n ≥ N . This complements a result of Eades et al. which in turn implies that if the positive integers s1, s2, . . . , s are all highly divisible by 2, then there is a ful...

The Hadamard conjecture is that Hadamard matrices exist for all orders 1,2, 4t where t 2 1 is an integer. We have obtained the following results which strongly support the conjecture: (i) Given any natural number q, there exists an Hadamard matrix of order 2 q for every s 2 [2log2 (q 3)]. (ii) Given any natural number q, there exists a regular symmetric Hadamard matrix with constant diagonal of...

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a...

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a...

Some new amicable orthogonal designs of order 8 are found as part of a complete search of the equivalence classes for orthogonal designs OD(8; 1, 1, 1, 1), OD(8; 1, 1, 1, 4), OD(8; 1, 1, 2, 2), OD(8; 1, 1, 1, 2), OD (8; 1, 1, 2, 4), OD(8; 1, 1, 1, 3), OD(8; 1, 1, 2, 3), OD(8; 1, 1, 1, 5) and OD(8; 1, 1, 3, 3). 2000 Mathematics subject classification (Amer. Math. Soc.): 05B30, 15A36.

When n2 elements are given, they can be arranged in the form of a square; similarly, when n8 elements (g ≥ 3 an integer) are given, they can be arranged in the form of a g-dimensional cube of side n (in short, a g-cube). The position of the elements can be indicated by g suffixes. Disciplines Physical Sciences and Mathematics Publication Details Hammer, J and Seberry, J, Higher dimensional orth...

In this paper we show the existence of new orthogonal designs, based on a number of new weighing matrices of order 2n and weights 2n − 5 and 2n−9 constructed from two circulants. These new weighing matrices were constructed recently by establishing various patterns on the locations of the zeros in a potential solution, in conjunction with the power spectral density criterion. We also demonstrat...

We find new full orthogonal designs in order 56 and show that of 1285 possible OD(56; s1, s2, s3, 56—s1—s2-s3) 163 are known, of 261 possible OD(56; s1, s2, 56—s1—s2) 179 are known. All possible OD(56; s1, 56 — s1) are known. Keywords : Construction, sequences, circulant matrices, amicable sets, orthogonal designs, AMS Subject Classification: Primary 05B15, 05B20, Secondary 62K05. Publication D...