Cwatset

A cwatset is a set of words in binary n-space which is closed with a twist.

That is, for each element c in a cwatset C, there exists some permutation p which, when applied to the results of c+C, results in C. Thus, all groups of binary words closed under bitwise addition are cwatsets whose permutation is the identity permutation.

One non-group example of a cwatset is

  F = {000,110,101}.

Note that

F + 000 = F

F + 110 = {110,011,011} = F with the first two components of each word transposed.

F + 101 = {101,011,000} = F with the first and third component of each word transposed.