Trace Representation of r-Ary Sequences Derived from Euler Quotients Modulo 2p

We introduce the r-ary sequence with period 2p2 derived from Euler quotients modulo 2p (p is an odd prime) where r is an odd prime divisor of (p-1). Then based on the cyclotomic theory and the theory of trace function in finite fields, we give the trace representation of the proposed sequence by det...

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Veröffentlicht in:IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Communications and Computer Sciences, 2021/12/01, Vol.E104.A(12), pp.1698-1703
Hauptverfasser: MOHAMMED, Rayan, DU, Xiaoni, JIN, Wengang, SUN, Yanzhong
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Sprache:eng
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Zusammenfassung:We introduce the r-ary sequence with period 2p2 derived from Euler quotients modulo 2p (p is an odd prime) where r is an odd prime divisor of (p-1). Then based on the cyclotomic theory and the theory of trace function in finite fields, we give the trace representation of the proposed sequence by determining the corresponding defining polynomial. Our results will be help for the implementation and the pseudo-random properties analysis of the sequences.
ISSN:0916-8508
1745-1337
DOI:10.1587/transfun.2021EAP1014