A Method of Finding Polynomials with Maximum Order on Polynomial Ring ☆

In recent times, the researches on cyclic multiplicative group over polynomial ring have had interesting results. Its applications are mainly for the construction of local cyclic codes; generate pseudo-random sequences; create keys for some symmetric key cryptosystem. Cyclic multiplicative group is generated from a generator polynomial and its order is also the order of generator polynomial. The determination of the maximum order of a polynomial is significant in determining the order of the other polynomials. So far, no specific method to identify if a polynomial has maximum order or not. This paper proposes a method to find polynomial with maximum order based on the order of a polynomial that is the multiplication of the other polynomials