> < ^ Date: Thu, 28 Apr 1994 12:58:00 +0200
> < ^ From: Frank Celler <frank.celler@math.rwth-aachen.de >
^ Subject: Blists

Dear Erik, Jasper & Reinald,

you wrote:

We want to use blists as a representation for binary codewords
because we hope it will be much faster than to use elements of
GF(2).

yes, at the moment this is most certainly true.

But we could not find a function for XOR(blist1, blist2) or
for NOT(blist1) which would make the functions we need (like our
function "distance") much faster. We now use

```BlistList(list1,[false])     instead of         Not(blist1)
```

but it is too slow. Are you implementing those functions in the
near future?

Have you tried to use the functions 'SubtractBlist' or 'DifferenceBlist'
(the latter is essentially "SubtractBlist( Copy(blist1), blist2 )")? The
function 'DifferenceBlist( b1, b2 )' will return a boolean list <d> such
that "d[i] = b1[i] and not b2[i]". If you keep a copy of an all true boolean
list, then "Not(b1) = DifferenceBlist( all_true, b1 )" and

gap> XorBlist := function( b1, b2 )
return UnionBlist(DifferenceBlist(b1,b2), DifferenceBlist(b2,b1));
end;
# or to avoid one copy and two functions calls
gap> XorBlist := function( b1, b2 )
local r;

```    r := Copy(b1);
SubtractBlist( r, b2 );
b2 := Copy(b2);
SubtractBlist( b2, b1 );
UniteBlist( r, b2 );
return r;
end;
gap> b1 := [ true, true, false, false ];
[ true, true, false, false ]
gap> b2 := [ true, false, true, false ];
[ true, false, true, false ]
gap> XorBlist( b1, b2 );
[ false, true, true, false ]
```

I admit that this will be a bit slower than a genuine 'XorBlist' but
it might be fast enough for your purpose. Please keep us informed.

best wishes
Frank

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