036: Fixed Length Error Correcting Codes

language Essence 1.3
$ prob036.essence: Fixed Length Error Correcting Codes
$ Problem details available at http://www.csplib.org/Problems/prob036/

given Character new type enum  ,
      maxDist       : int(1..) ,        $ maxDist is the maximum distance between two characters
      codeWordLength : int(1..),
      numOfCodeWords : int(1..)

letting Index be domain int(1..codeWordLength),
        String be domain function (total) Index --> Character

given dist : function (Character, Character) --> int(0..maxDist),
      minDist : int(0..maxDist * codeWordLength)

find c : set (size numOfCodeWords) of String

such that
    forAll s1, s2 in c
        , s1 != s2
        . (sum i : Index . dist((s1(i),s2(i)))) >= minDist