Universidade de Santiago de Compostela, Servicio de Publicaciones
Abstract
Three algorithms looking for pretty large partial Hadamard ma-
trices are described. Here “large” means that hopefully about a third of a
Hadamard matrix (which is the best asymptotic result known so far, [8]) is
achieved. The first one performs some kind of local exhaustive search, and
consequently is expensive from the time consuming point of view. The second
one comes from the adaptation of the best genetic algorithm known so far
searching for cliques in a graph, due to Singh and Gupta [21]. The last one
consists in another heuristic search, which prioritizes the required processing
time better than the final size of the partial Hadamard matrix to be obtained. In
all cases, the key idea is characterizing the adjacency properties of vertices in a
particular subgraph Gt of Ito’s Hadamard Graph (4t) [18], since cliques of
order m in Gt can be seen as (m + 3) × 4t partial Hadamard matrices.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM-016Junta de Andalucía P07-FQM-0298
