055: Equidistant Frequency Permutation Arrays

language Essence 1.3
$ Equidistant Frequency Permutation Arrays.
$ Details available from CP paper. 

given numChars       : int(1..)        $ aka q, the number of symbols.
given lam            : int(1..)        $ aka lambda, the number of each symbol in a word.
given numCodeWords   : int(1..)        $ aka v
given dist           : int(1..)        $ aka d, the hamming distance between all pairs of words. 

letting Character be domain int(1..numChars)

letting wordLength be lam*numChars

letting Index be domain int(1..wordLength)

letting String be domain function (total) Index --> Character

find c : set (size numCodeWords) of String

$ each codeword must contain each symbol lambda times.
such that
    forAll s in c . forAll a : Character .
        ( (sum i : Index . toInt(s(i)=a) )=lam)

$ each pair of codewords must differ in exactly d places.
such that
    forAll s1, s2 in c .
        s1 != s2 -> (sum i : Index . toInt(s1(i)!=s2(i))) = dist