Irreducible congruences over $\textrm {GF}(2)$

Abstract:

In characterizing and determining the number of conjugate sets of irreducible congruences of degree m belonging to $GF(p)$ relative to the group $G(p)$ of linear fractional transformations with coefficients belonging to the same field, the case $p = 2$ has been consistently excluded from considerations. In this paper we consider the special case $p = 2$ and determine the number of conjugate sets of m-ic congruences belonging to $GF(2)$ relative to $G(2)$.