New Sequences with Zero Autocorrelation

被引：4

作者：

E. M. Gabidulin

V. V. Shorin

机构：

来源：

Problems of Information Transmission | 2002年 / 38卷 / 4期

关键词：

Autocorrelation; System Theory; Search Method; Exhaustive Search; Algebraic Number;

D O I：

10.1023/A:1022093728009

中图分类号：

学科分类号：

摘要：

New families of unimodular sequences of length p = 3f + 1 with zero autocorrelation are described, p being a prime. The construction is based on employing Gauss periods. It is shown that in this case elements of the sequences are algebraic numbers defined by irreducible polynomials over ℤ of degree 12 (for the first family) and 6 (for the second family). In turn, these polynomials are factorized in some extension of the field ℚ into polynomials of degree, respectively, 4 and 2, which are written explicitly. For p = 13, using the exhaustive search method, full classification of unimodular sequences with zero autocorrelation is given.

引用

页码：255 / 267

页数：12

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