TY - GEN

T1 - A binarization of geometric sequences with Legendre symbol and its autocorrelation

AU - Nogami, Yasuyuki

AU - Tada, Kazuki

AU - Uehara, Satoshi

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Let p be an odd characteristic and m be the degree of primitive polynomial f(x). Let ω be its zero, that is a primitive element in F pm*, then the sequence S =si, si = Tr (ωi) for i = 0, 1, 2,... becomes a maximum length sequence, where Tr (·) is the trace function over Fp. On this fact, this paper proposes to binarize the sequence by using Legendre symbol. It will be a class of geometric sequences but its properties such as the period and autocorrelation has not been discussed. Then, it is shown that the obtained binary sequence (geometric sequence with Legendre symbol) has the period L given by 2(pm - 1)/(p-1) and a certain periodic autocorrelation. After that, this paper also shows the numbers of ones and minus ones in the proposed binary sequence per a period together with some small examples.

AB - Let p be an odd characteristic and m be the degree of primitive polynomial f(x). Let ω be its zero, that is a primitive element in F pm*, then the sequence S =si, si = Tr (ωi) for i = 0, 1, 2,... becomes a maximum length sequence, where Tr (·) is the trace function over Fp. On this fact, this paper proposes to binarize the sequence by using Legendre symbol. It will be a class of geometric sequences but its properties such as the period and autocorrelation has not been discussed. Then, it is shown that the obtained binary sequence (geometric sequence with Legendre symbol) has the period L given by 2(pm - 1)/(p-1) and a certain periodic autocorrelation. After that, this paper also shows the numbers of ones and minus ones in the proposed binary sequence per a period together with some small examples.

KW - Legendre symbol

KW - odd characteristic

KW - primitive polynomial

KW - trace

UR - http://www.scopus.com/inward/record.url?scp=84904540690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904540690&partnerID=8YFLogxK

U2 - 10.1109/IWSDA.2013.6849054

DO - 10.1109/IWSDA.2013.6849054

M3 - Conference contribution

AN - SCOPUS:84904540690

SN - 9781467364812

T3 - IWSDA 2013 - 6th International Workshop on Signal Design and Its Applications in Communications

SP - 28

EP - 31

BT - IWSDA 2013 - 6th International Workshop on Signal Design and Its Applications in Communications

PB - IEEE Computer Society

T2 - 6th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2013

Y2 - 27 October 2013 through 1 November 2013

ER -