The additive index of polynomials over finite fields

In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We show that every polynomial P(x)∈Fq[x] can be expressed uniquely in its additive index form such that P(x)=f(L(x))+M(x) where L(x),M(x) are p-linearized polynomials over Fq, deg⁡(M)

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Bibliographic Details
Published in:Finite fields and their applications 2022-03, Vol.79, p.102002, Article 102002
Main Authors: Reis, Lucas, Wang, Qiang
Format: Article
Language:English
Subjects:
Character sums
Finite fields
Index
Linearized polynomials
Permutation polynomials
Value sets
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Summary:In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We show that every polynomial P(x)∈Fq[x] can be expressed uniquely in its additive index form such that P(x)=f(L(x))+M(x) where L(x),M(x) are p-linearized polynomials over Fq, deg⁡(M)
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2022.102002