TY - GEN
T1 - An efficient generation of geometric sequences defined with trace and legendre symbol
AU - Nogami, Yasuyuki
AU - Tada, Kazuki
AU - Uehara, Satoshi
N1 - Publisher Copyright:
© 2014 IEICE.
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 -