Linear Complexity of Designs based on Coordinate Sequences of LRS and on Digital Sequences of Matrix/Skew LRS Coordinate Sequences over Galois Ring

This article continues investigation of ways to obtain pseudo-random sequences over Galois field via generating LRS over Galois ring and complication it. Previous work is available at http://eprint.iacr.org/2016/212 In this work we provide low rank estimations for sequences generated by two different designs based on coordinate sequences of linear recurrent sequences (LRS) of maximal period (MP) over Galois ring R = GR(pn, r), p ≥ 5, r ≥ 2, with numbers s such that s = kr+2, k ∈ N0, and based on digital sequences of coordinate sequences of matrix/skew MP LRS over such Galois rings.