Two-Dimensional Sequences of Primitive Polynomials

In this paper, we consider the two-dimensional sequence of primitive polynomials, which is defined by two positive integers and a primitive polynomial. The concept of \(q^m\) conjugate order is used to describe the two-dimensional sequence. Using the two-dimensional sequences, we can find maximum period primitive-polynomial sequences for more values of degrees than using the one-dimensional sequences. Examples of the applications of the two-dimensional sequence by computer search are shown.