A binarization of geometric sequences with Legendre symbol and its autocorrelation

Yasuyuki Nogami, Kazuki Tada, Satoshi Uehara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationIWSDA 2013 - 6th International Workshop on Signal Design and Its Applications in Communications
PublisherIEEE Computer Society
Pages28-31
Number of pages4
ISBN (Print)9781467364812
DOIs
Publication statusPublished - 2013
Event6th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2013 - Tokyo, Japan
Duration: Oct 27 2013Nov 1 2013

Other

Other6th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2013
CountryJapan
CityTokyo
Period10/27/1311/1/13

Fingerprint

Binary sequences
Autocorrelation
Polynomials

Keywords

  • Legendre symbol
  • odd characteristic
  • primitive polynomial
  • trace

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Signal Processing

Cite this

Nogami, Y., Tada, K., & Uehara, S. (2013). A binarization of geometric sequences with Legendre symbol and its autocorrelation. In IWSDA 2013 - 6th International Workshop on Signal Design and Its Applications in Communications (pp. 28-31). [6849054] IEEE Computer Society. https://doi.org/10.1109/IWSDA.2013.6849054

A binarization of geometric sequences with Legendre symbol and its autocorrelation. / Nogami, Yasuyuki; Tada, Kazuki; Uehara, Satoshi.

IWSDA 2013 - 6th International Workshop on Signal Design and Its Applications in Communications. IEEE Computer Society, 2013. p. 28-31 6849054.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nogami, Y, Tada, K & Uehara, S 2013, A binarization of geometric sequences with Legendre symbol and its autocorrelation. in IWSDA 2013 - 6th International Workshop on Signal Design and Its Applications in Communications., 6849054, IEEE Computer Society, pp. 28-31, 6th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2013, Tokyo, Japan, 10/27/13. https://doi.org/10.1109/IWSDA.2013.6849054
Nogami Y, Tada K, Uehara S. A binarization of geometric sequences with Legendre symbol and its autocorrelation. In IWSDA 2013 - 6th International Workshop on Signal Design and Its Applications in Communications. IEEE Computer Society. 2013. p. 28-31. 6849054 https://doi.org/10.1109/IWSDA.2013.6849054
Nogami, Yasuyuki ; Tada, Kazuki ; Uehara, Satoshi. / A binarization of geometric sequences with Legendre symbol and its autocorrelation. IWSDA 2013 - 6th International Workshop on Signal Design and Its Applications in Communications. IEEE Computer Society, 2013. pp. 28-31
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