The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Binary pseudorandom sequences of period $2^{m}-1$ with ideal autocorrelation generated by the polynomial $z^{d}+(z+1)^{d}$

다항식 $z^{d}+(z+1)^{d}$에 의해 발생된 이상적인 자기상관을 갖는 주기 $2^{m}-1$의 이진 의사불규칙 시퀀스

  • 노종선 (건국대학교 전자공학과) ;
  • 정하봉 (홍익대학교 전기전자공학부) ;
  • 윤민선 (건국대학교 전자공학과)
  • Published : 1998.05.01
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Abstract

In this paper, we present a construction for binary pseudorandom sequences of period $2^{m}-1$ with ideal autocorraltion property using the polynomial $z^{d}+(z+1)^{d}$. We show that the sequence obtained from the polynomial becomes an m-sequence for certain values of d. We also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is $3k{\pm}1$, where k is a positive integer. These new sequences are represented using trace function and the results are tabulated.

본 논문에서는 다항식 $z^{d}+(z+1)^{d}$를 이용하여 이상적인 자기상관특성을 갖는 주기 $2^{m}-1$의 이진 의사불규칙시퀀스를 구성하는 것을 보였다. 다항식으로부터 얻어진 시퀀스는 어떤 d값에서는 m-시퀀스가된다. 또한 k가 양의 정수이고 m이 $3k{\pm}1$일 때 이상적인 자기상관특성을 갖는 새로운 이진 시퀀스를 산출하는 몇몇의 d값을 발견했다. 이들 새로운 시퀀스는 trace함수를 이용하여 표현하였으며 그 결과들을 표로 나타내었다.

Keywords

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