3 research outputs found
The merit factor of binary arrays derived from the quadratic character
We calculate the asymptotic merit factor, under all cyclic rotations of rows
and columns, of two families of binary two-dimensional arrays derived from the
quadratic character. The arrays in these families have size p x q, where p and
q are not necessarily distinct odd primes, and can be considered as
two-dimensional generalisations of a Legendre sequence. The asymptotic values
of the merit factor of the two families are generally different, although the
maximum asymptotic merit factor, taken over all cyclic rotations of rows and
columns, equals 36/13 for both families. These are the first non-trivial
theoretical results for the asymptotic merit factor of families of truly
two-dimensional binary arrays.Comment: minor correction