On the Crosscorrelation of m Sequence over Finite Field and Its Decimation Sequence

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On the Crosscorrelation of m Sequence over Finite Field and Its Decimation Sequence

更新时间：2025-07-16

- On the Crosscorrelation of m Sequence over Finite Field and Its Decimation Sequence
- Acta Electronica Sinica Vol. 28, Issue 10, Pages: 69-73(2000)
- 作者机构：
  
  北京邮电大学信息安全中心126信箱,北京,100876
- 作者简介：
- 基金信息：
- DOI：
  CLC： G202
- Published：2000
- 稿件说明：
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On the Crosscorrelation of m Sequence over Finite Field and Its Decimation Sequence[J]. Acta Electronica Sinica, 2000, 28(10): 69-73.
DOI：

On the Crosscorrelation of m Sequence over Finite Field and Its Decimation Sequence[J]. Acta Electronica Sinica, 2000, 28(10): 69-73. DOI：

摘要

本文研究了有限域GF(p)上的m序列与其采样序列之间的互相关函数C

(t)

得到以下结论:(1)当采样因子d= p

+1 p+1 + p

-1 2

n为奇数且p≡3(mod 4)时

|1+C

(t)| 1+p 2 p

从而解决了Muller在文献中提出的一个公开问题

并将文献[1

]

中的p=3时的结论推广为一般情形;(2)当d= p

+1 p+1

n为奇数且p≡3(mod 4)时

(t)∈{-1

-1+ p

n+1 -1- p

n+1

};(3)在以上两种情况下

对|1+C

(t)|关于t的分布进行了研究

结果表明

当p很大时

|1+C

(t)|取最大值的概率很小.

Abstract

In this paper we investigate the crosscorrelation function C

(t) of m sequence on finite field GF(p) and its decimation sequence

and get the following results:(1)For decimation factor d= p

+1 p+1 + p

-1 2

p≡3(mod 4)

n odd

we show that |1+C

(t)| 1+p 2 p

and therefore solve an open problem raised by Muller in [1

]

and generalize the result proved in [1

]

;(2)For decimation factor d= p

+1 p+1

n odd

p≡3(mod 4)

we show C

(t)∈{-1

-1+ p

n+1

-1- p

n+1

};(3)In the two cases above

we study the distribution of |1+C

(t)| with respect to t

and obtain that when p is big enough

the

probability of |1+C

(t)| achieving the maximum is very small.

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