Enumeration of the Semilinear Isometry Classes of Linear Codes
Harald Fripertinger · 2005
In joint papers with A. Kerber we showed how to enumerate the linear isometry classes of linear codes by certain substitutions into cycle index polynomials of the action of projective linear groups on projective spaces. In the present paper it is described how to gen-eralize this approach to the enumeration of the semilinear isometry classes. Moreover, we motivate that with respect to error correcting properties semilinear isometry is the natural equivalence relation on the set of all linear codes. 1