한국전자통신학회논문지 (The Journal of the Korea institute of electronic communication sciences)

한국전자통신학회 (Korea Institute of Electronic Communication Science)
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GF(2n)위에서 x5+bx3+b2mx2+1=0의 서로 다른 해의 개수

Number of Different Solutions to x5+bx3+b2mx2+1=0 over GF(2n)

  • 투고 : 2013.09.11
  • 심사 : 2013.11.15
  • 발행 : 2013.11.30
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⟨ 이전 논문 다음 논문 ⟩

초록

주기가 $2^n-1$인 이진수열은 부호이론, CDMA와 같은 통신시스템과 암호체계 등 많은 분야에서 폭넓게응용되고 있다. 본 논문에서는 n=2m, m=4k($k{\geq}2$)이고 $d=3{\cdot}2^m-2$일 때 생성되는 비선형 이진수열의 상호상관관계의 빈도를 분석하기 위해 $GF(2^n)$ 위에서 방정식 $x^5+bx^3+b^{2^m}x^2+1=0$의 해의 유형에 대하여 분석하고 서로 다른 해의 개수를 결정하는 알고리즘을 제안한다.

Binary sequences of period $2^n-1$ are widely used in many areas of engineering and sciences. Some well-known applications include coding theory, code-division multiple-access (CDMA) communications, and stream cipher systems. In this paper we analyze different solutions to $x^5+bx^3+b^{2^m}x^2+1=0$ over $GF(2^n)$. The number of different solutions determines frequencies of cross-correlations of nonlinear binary sequences generated by $d=3{\cdot}2^m-2$, n=2m, m=4k($k{\geq}2$). Also we give an algorithm for determination of number of different solutions to the equation.

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참고문헌

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