Finding Enumerators for Generalized (L, G)-Code

Abstract

The algorithm for finding the enumerators of degree 2 and higher for the generalized (L, G)‑code is presented. This algorithm makes it possible to enhance the rate of finding enumerators as distinct from the exhaustive search algorithm. It can be used to construct a modern variant of the McEliece cryptosystem. The presented solution is based on using the representation of the Galois field element via the function containing the coefficients of a smaller field. In addition, the results of comparison of the modern McEliece cryptosystem constructed based on the Goppa codes and generalized (L, G)-codes are presented.