In the present paper, a new characterization of orthogonality monic polynomials sequence $\left\{ Q_{n}\right\} _{n\geq 0}$ is obtained. This defined as linear combination another orthogonal P_{n}\right\} such as% \begin{equation*} Q_{n}(x)+r_{n}Q_{n-1}(x)=P_{n}(x)+s_{n}P_{n-1}(x)+t_{n}P_{n-2}\left( x\right) +v_{n}P_{n-3}\left( +w_{n}P_{n-4}(x),\ n\geq 0 \end{equation*}% where $w_{n}r_{n}\neq 0...

Symmetric 2-adic complexity is a better measure for assessing the strength of periodic binary sequence against rational approximation attack. We study symmetric sequences with known complexity. To this end, we propose an equivalent definition and two sufficient conditions to achieve maximum As first application, several types are easily shown have In addition, new definition, by analysing algeb...