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Diskretn. Anal. Issled. Oper., 2018, Volume 25, Number 4, Pages 59–80 (Mi da909)  

Permutation binomial functions over finite fields

A. V. Miloserdov

Novosibirsk State University, 1 Pirogov St., 630090 Novosibirsk, Russia

Abstract: We consider binomial functions over a finite field of order $2^n$. Some necessary condition is found for such a binomial function to be a permutation. It is proved that there are no permutation binomial functions in the case that $2^n-1$ is prime. Permutation binomial functions are constructed in the case when $4n$ is composite and found for $n\le8$. Tab. 2, bibliogr. 30.

Keywords: vectorial Boolean function, binomial function, permutation, APN function.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-31-00374
18-07-01394
Ministry of Education and Science of the Russian Federation 1.12875.2018/12.1
5-100
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.5.1, 0314-2016-0017
The author was supported by the Russian Foundation for Basic Research (projects nos. 18-31-00374 and 18-07-01394), the Ministry of Education and Science (task no. 1.12875.2018/12.1 and Program 5-100), and Program of Basic Scientific Research no. I.5.1 of the Siberian Branch of the Russian Academy of Sciences (project no. 0314-2016-0017).


DOI: https://doi.org/10.17377/daio.2018.25.611

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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:4, 694–705

Document Type: Article
UDC: 519.8
Received: 20.02.2018
Revised: 04.06.2018

Citation: A. V. Miloserdov, “Permutation binomial functions over finite fields”, Diskretn. Anal. Issled. Oper., 25:4 (2018), 59–80; J. Appl. Industr. Math., 12:4 (2018), 694–705

Citation in format AMSBIB
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\paper Permutation binomial functions over finite fields
\jour Diskretn. Anal. Issled. Oper.
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\pages 59--80
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\transl
\jour J. Appl. Industr. Math.
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\issue 4
\pages 694--705
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