On derivatives of polynomials over finite fields through integration

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• 作者：E. Pasalic^a ; ^{enes.pasalic6@gmail.com} ; A. Muratović-Ribić^b ; ^{amela@pmf.unsa.ba} ; S. Hodzić^c ; ^{samir_hodzic89@hotmail.com} ; S. Gangopadhyay^d ; ^{gsugata@gmail.com}
• 关键词：Finite fields ; Boolean functions ; Derivatives ; Linear structures ; Planar mappings
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：30 January 2017
• 年：2017
• 卷：217
• 期：part_P2
• 页码：294-303
• 全文大小：408 K
• 卷排序：217

文摘

In this article, using rather elementary technique and the derived formula that relates the coefficients of a polynomial over a finite field and its derivative, we deduce many interesting results related to derivatives of Boolean functions and derivatives of mappings over finite fields. For instance, we easily identify several infinite classes of polynomials which cannot possess linear structures. The same technique can be applied for deducing a nontrivial upper bound on the degree of so-called planar mappings.