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Title: Polynomial addition sets of degree 3
Keywords: Polynomial Addition set
Issue Date: 2-May-2008
Citation: ZHAN YANXIN (2008-05-02). Polynomial addition sets of degree 3. ScholarBank@NUS Repository.
Abstract: Let G be a finite group of order v > 1. Let f(x) be an integral polynomial. A subsetD of G with k elements is a (v, k, f(x))-polynomial addition set if f(D) =N; Gwhere D is in Z[G] and is the sum of the elements d in G, G is in Z[G] and is the sum of elements g in G and N; is an integer. We call an integralpolynomial primitive if the gcd of its coefficients is equal to 1.In general, there exists many polynomials that satisfy the above condition.Among these polynomials, we fix a primitive one with least degree. We call thispolynomial the minimal polynomial of D and its degree is called the degree ofD. Characterization of degree 3 polynomial addition sets in cyclic groups G has not been done before and will be the main focus in this thesis.
Appears in Collections:Master's Theses (Open)

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