A Method of Finding Polynomials with Maximum Order on Polynomial Ring

Authors: Nguyễn Trung Hiếu*, Ngô Đức Thiện

Abstract

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

Keyword

Local Cyclic Code, Cyclic Multiplicative Group, polynomial ring.
Pages : 75-80

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