具有非正自相关函数的二进制序列

王可; Lloyd; R.Welch

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具有非正自相关函数的二进制序列

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- 具有非正自相关函数的二进制序列
- Binary Sequences with Non-Positive Autocorrelation Values
- 电子学报 1982年第5期页码：10-17
- 作者机构：
  
  1.   Lloyd R. Welch
  2.   Professor of Electrical Engineering at the University of Southern California
  3.   Los Angeles
  4.   California .  ,90007
- 作者简介：
- 基金信息：
- DOI：
  中图分类号：
- 纸质出版：1982
- 稿件说明：
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[1]王可,,,,,,,,,Lloyd,R.Welch.具有非正自相关函数的二进制序列[J].电子学报,1982(05):10-17.

王可, Lloyd, R.Welch. Binary Sequences with Non-Positive Autocorrelation Values[J]. Acta Electronica Sinica, 1982, (5): 10-17.
[1]王可,,,,,,,,,Lloyd,R.Welch.具有非正自相关函数的二进制序列[J].电子学报,1982(05):10-17. DOI：

王可, Lloyd, R.Welch. Binary Sequences with Non-Positive Autocorrelation Values[J]. Acta Electronica Sinica, 1982, (5): 10-17. DOI：

摘要

<正> Baumert[2] developed the theory of binary sequences with the property of transorthogonality and orthogonality for cyclic shifts. Turyn[3] investigated the existence of binary sequences with small autocorrelation values in terms of min max|aj | where a1 is theperiodic correlation and the minimization is over binary sequences of fixed length. In this paper we restrict the investigation to cyclic correlation and drop the absolute value sign in the min max expression.In this study many binary sequences were found with autocorrelation properties in between transorthogonality and orthogonality. The most interesting sequences were those we named Yin-Yang sequences whose out of phase correlations are zero except for r equal to one half the period when the value is negative. Within this class

an infinite family is constructed.An exhaustive list of binary sequences with non-positive out of phase autocorrelation for lengths 4

40 was obtained by computer search and presented at the end of th

Abstract

Baumert[2] developed the theory of binary sequences with the property of transorthogonality and orthogonality for cyclic shifts. Turyn[3] investigated the existence of binary sequences with small autocorrelation values in terms of min max|aj | where a1 is theperiodic correlation and the minimization is over binary sequences of fixed length. In this paper we restrict the investigation to cyclic correlation and drop the absolute value sign in the min max expression.In this study many binary sequences were found with autocorrelation properties in between transorthogonality and orthogonality. The most interesting sequences were those we named Yin-Yang sequences whose out of phase correlations are zero except for r equal to one half the period when the value is negative. Within this class

an infinite family is constructed.An exhaustive list of binary sequences with non-positive out of phase autocorrelation for lengths 4

40 was obtained by computer search and presented at the end of this paper.

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