Equidistant filters based on skew ML-sequences over fields

Let $p$ be a prime number, $R = \mathrm{GF}(q)$ be a field of $q = p^r$ elements and $S = \mathrm{GF}(q^n)$ be an extension of $R$. Let $\breve{S}$ be the ring of all linear transformations of the space $_RS$. A linear recurring sequence $v$ of order $m$ over the module $_{\breve{S}}S$ is said to be a skew linear recurring sequence (skew LRS) of order $m$ over $S$. The period $T(v)$ of such sequence satisfies the inequality $T(v) \leqslant\tau = q^{mn}-1$. If $T(v) = \tau$ we call $v$ a skew LRS of maximal period (skew MP LRS). Here we investigate periodic properties and rank (linear complexity) of the sequence $y(i) = v(i)v(i + k)\cdot\ldots\cdot v(i + k(s-1))$, $k, s \in \mathbb{N}_0$, $i\geqslant 0$, where $v$ is a skew MP LRS. Based on the obtained results we propose new methods for filtering generators construction based on skew MP LRS.