Second order linear sequence subgroups in finite fields—II

In previous papers [O.J. Brison, J.E. Nogueira, Linear recurring sequence subgroups in finite fields, Finite Fields Appl. 9 (2003) 413–422; O.J. Brison, J.E. Nogueira, Second order linear sequence subgroups in finite fields, Finite Fields Appl. 14 (2008) 277–290] the authors investigated when, and how, a multiplicative subgroup of a finite field can be written, without repetition, as a cyclically-closed second order recurring sequence. Here, the earlier results are extended for sequences with certain restricted periods.