TY - GEN

T1 - An efficient generation of geometric sequences defined with trace and legendre symbol

AU - Nogami, Yasuyuki

AU - Tada, Kazuki

AU - Uehara, Satoshi

PY - 2014/12/8

Y1 - 2014/12/8

N2 - Let p and m be an odd characteristic and extension degree, respectively. Then, let ! be a primitive element in F∗pm, a geometric sequence S = Lsir, si =(Tr(ωi)/p) for i = 0, 1, 2,... has been proposed together with its some properties, where Tr (·) is the trace function over Fp and (a/p) is Legendre symbol for a in Fp. This paper shows an efficient method for generating the sequence when the base field Fpm is defined by an irreducible binomial over Fp with small odd characteristic p.

AB - Let p and m be an odd characteristic and extension degree, respectively. Then, let ! be a primitive element in F∗pm, a geometric sequence S = Lsir, si =(Tr(ωi)/p) for i = 0, 1, 2,... has been proposed together with its some properties, where Tr (·) is the trace function over Fp and (a/p) is Legendre symbol for a in Fp. This paper shows an efficient method for generating the sequence when the base field Fpm is defined by an irreducible binomial over Fp with small odd characteristic p.

KW - Legendre symbol

KW - irreducible binomial

KW - odd characteristic

KW - primitive element

KW - trace

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M3 - Conference contribution

AN - SCOPUS:84920527989

T3 - Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014

SP - 719

EP - 721

BT - Proceedings of 2014 International Symposium on Information Theory and Its Applications, ISITA 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 International Symposium on Information Theory and Its Applications, ISITA 2014

Y2 - 26 October 2014 through 29 October 2014

ER -