On the cyclicity of Goppa codes, parity-check subcodes of Goppa codes, and extended Goppa codes
Let \(K\) be an extension field of a prime finite field. A semilinear transformation on \(K^n\) is the action of a permutation of coordinates in \(K^n\) followed by an automorphism of the field \(K\). An induced-cyclic code is a code for which the cyclic property comes from a semilinear transformation. The paper contains the determination of all induced-cyclic Goppa codes. It also gives a necessary and sufficient condition for a Goppa code to have an induced-cyclic extension. Extensions of Goppa codes are shown to be alternant codes.
scientific article; zbMATH DE number 1538400