1,357 research outputs found
Computing random -orthogonal Latin squares
Two Latin squares of order are -orthogonal if, when superimposed,
there are exactly distinct ordered pairs. The spectrum of all values of
for Latin squares of order is known. A Latin square of order is
-self-orthogonal if and its transpose are -orthogonal. The spectrum
of all values of is known for all orders . We develop randomized
algorithms for computing pairs of -orthogonal Latin squares of order and
algorithms for computing -self-orthogonal Latin squares of order
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Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results
We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of mutually orthogonal Latin squares of order to construct a set of mutually orthogonal Latin squares of order
Constructions of Pairs of Orthogonal Latin Cubes
A pair of orthogonal latin cubes of order is equivalent to an MDS code
with distance or to an orthogonal array. We construct
pairs of orthogonal latin cubes for a sequence of previously unknown orders
and . The minimal new obtained parameters
of orthogonal arrays are .
Keywords: latin square, latin cube, MOLS, MDS code, block design, Steiner
system, orthogonal arrayComment: New pairs of orthogonal latin 3-cubes are available on the website
https://ieee-dataport.org/open-access/graeco-latin-cube
Sets of three pairwise orthogonal Steiner triple systems
AbstractTwo Steiner triple systems (STS) are orthogonal if their sets of triples are disjoint, and two disjoint pairs of points defining intersecting triples in one system fail to do so in the other. In 1994, it was shown (Canad. J. Math. 46(2) (1994) 239–252) that there exist a pair of orthogonal Steiner triple systems of order v for all v≡1,3 (mod6), with v⩾7, v≠9. In this paper we show that there exist three pairwise orthogonal Steiner triple systems of order v for all v≡1(mod6), with v⩾19 and for all v≡3(mod6), with v⩾27 with only 24 possible exceptions
Applications of Hadamard matrices, Journal of Telecommunications and Information Technology, 2003, nr 2
We present a number of applications of Hadamard matrices to signal processing, optical multiplexing, error correction coding, and design and analysis of statistics
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