Open AccessAbout the values of generating polynomials of cyclotomic classes
Author(s) -
Vladimir Edemskiy,
A S Tsurina
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1352/1/012014
Subject(s) - mathematics , cyclotomic polynomial , trace (psycholinguistics) , binary number , representation (politics) , order (exchange) , pseudorandom number generator , pseudorandom binary sequence , discrete mathematics , arithmetic , algebra over a field , combinatorics , pure mathematics , polynomial , algorithm , mathematical analysis , philosophy , linguistics , finance , politics , political science , law , economics
The trace representation of sequences is a powerful tool for the analysis and for the design of pseudorandom sequences. Z. Dai et al. (2011) reduce the problem of determining trace representation of series of binary e th power residue sequences to that of determining the values of generating polynomials of cyclotomic classes. We derive the values of generating polynomials of cyclotomic classes of order 4, 6, 8 and consequently solve three problems pointed by Z. Dai et al. In fact, we study the discrete Fourier transform of cyclotomic sequences of order 4, 6, 8.