h(a,b) =s_{b}- # (s_{a}s_{b}) - #({1,...,b \s_{a}s_{b}).

fun hamming bits distance numsymbols space = let val xs = List.tabulate(numsymbols,(fn x => FS.upperBound(space,#[(1,bits)]))) val tmp = FS.Value.make(space,#[(1,bits)]) fun minDist(x,y)= let val tmp1 = FS.setvar space val tmp2 = FS.setvar space val tmp3 = FS.setvar space val tmp4 = FD.intvar(space,#[(0,bits)]) val tmp5 = FD.intvar(space,#[(0,bits)]) in (FS.relOp(space,x,FS.INTER,y,FS.SEQ,tmp1); FS.relOp(space,x,FS.UNION,y,FS.SEQ,tmp2); FS.relOp(space,tmp,FS.MINUS,tmp2,FS.SEQ,tmp3); FS.cardinality(space,tmp1,tmp4); FS.cardinality(space,tmp3,tmp5); post(space,`bits `- FD(tmp4) `- FD(tmp5) `>= `distance,FD.DOM)) end fun forallTail([y])= () | forallTail(y::ys) = (List.app(fn x => minDist(y,x))(ys);forallTail ys) in forallTail(xs); FS.setvarbranch(space,Vector.fromList xs, FS.FSB_NONE,FS.FSB_MIN); xs end

The Script in Listing 27 generates a Hamming code for numsymbols symbols in words with bits bits and a Hamming distance of distance. The procedure minDist implements the constraint that the Hamming distance does not exceed the value of distance. The list xs holds the sets representing the single codes. The nested loop forallTail imposes minDist on all pairwise distinct elements of xs. The branching employs straightforwardly a naive strategy.

The following code generates a Hamming code for 16 symbols using 7 bit words and ensures a Hamming distance of 2.

val distance = 2 val bits = 7 val numsymbols = 16 let val(s,r) = valOf(Search.searchOne (hamming bits distance numsymbols)) in List.map(fn y => domainToList y) (List.map(fn x =>FS.Reflect.upperBound(s,x))r) end

Andreas Rossberg 2006-08-28