Codes derived from binary Goppa codes (Q1347392)

In this paper, a new family of codes based on binary Goppa codes with a special automorphism group has been constructed. The special group is such that if the coefficients of a Goppa polynomial belong to some subfield of the field \(\text{GF}(2^m)\), then the automorphism group of the code contains the group generated by the Frobenius automorphism. From the set of elements of the code that are invariant under the action of the Frobenius group, a code of smaller length, called an \(s\)-projected code, is derived. Bounds on the dimension and minimum distance for this new family of codes are obtained. Also, a polynomial-time algorithm of decoding up to the designated distance has been constructed.