# Schur ring and Codes for S-subgroups over _2^n

In this paper the relationship between S-subgroups in _2^n and binary codes is shown. If the codes used are both P(T)-codes and G-codes, then the S-subgroup is free. The codes constructed are cyclic, decimated or symmetric and the S-subgroups obtained are free under the action the cyclic permutation subgroup, invariants under the action the decimated permutation subgroup and symmetric under the action of symmetric permutation subgroup, respectively. Also it is shows that there is no codes generating whole _2^n in any _n(a)-complete S-set of the S-ring S(_2^n,S_n).

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