055: Equidistant Frequency Permutation Arrays

language ESSENCE 1.3.0

$ Problem Equidistant Frequency Permutation Arrays
$
$ Problem details available at http://www.csplib.org/Problems/prob055/
$
$ Essence model by Andrew Martin
$
$ Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/

given v : int(1..)
given d : int(1..)
given q : int(1..)
given lam : int(1..)

letting dSequnce be domain int(1..q*lam)
letting dElement be domain int(1..q)

find E : set (size v) of matrix indexed by [dSequnce] of dElement

$ each element in (1..q) must occur lambda times per sequence
such that
    forAll m in E .
        forAll element : dElement .
            (sum index : dSequnce . toInt(m[index] = element)) = lam

$ each non-identical pair must be hamming distance d apart
such that
    forAll seqA, seqB in E .
        seqA = seqB
        \/
        (sum index : dSequnce . toInt(seqA[index] != seqB[index])) = d