New families of binary sequences with low correlation

New families of binary sequences with low correlation
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DOI：
10.1109/tit.2003.818399
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发表时间：
2003-11
期刊：
IEEE Trans. Inf. Theory
影响因子：
--
通讯作者：
Sang-Hyo Kim;Jong-Seon No
Sang-Hyo Kim;Jong-Seon No
中科院分区：
其他
文献类型：
--
作者：
Sang-Hyo Kim;Jong-Seon No

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对于正整数\(n\)，提出了周期为\(2^{n}-1\)且具有低相关性的二进制序列的新族\(S\)和\(U\)，其中对于某个正整数\(e\)，当\(n/e\)为奇数时定义族\(S\)，当\(n/e\)为偶数时定义族\(U\)。族\(S\)具有四值相关性，并且是\(S. 博兹塔斯\)和\(P.V. 库马尔\)（见同刊，第\(40\)卷，第\(532 - 537\)页，\(1994\)年）所引入的类戈尔德序列族的推广。族\(U\)也是\(P. 乌达亚\)（《从有限环得到的多相和跳频序列》，博士论文，印度理工学院坎普尔分校电气工程系，\(1992\)年）所定义的序列族的推广，具有六值相关性。类戈尔德序列与戈尔德序列之间的关系，与族\(S\)和由\(R. 戈尔德\)（见同刊，第\(IT - 14\)卷，第\(154 - 156\)页，\(1968\)年）、\(T. 卡萨米\)（见伊利诺伊大学厄巴纳 - 香槟分校协调科学实验室，技术报告\(R - 285\)，\(AD632574\)，\(1966\)年）以及韦尔奇部分贡献的二进制序列所构造的族之间的关系相同。利用提升思想（诺，\(J. - S.\)和库马尔，\(P.V.\)，见同刊，第\(35\)卷，第\(371 - 379\)页，\(1989\)年）对族\(S\)和\(U\)，还构造了具有相同相关性分布和大线性跨度的二进制序列族。
For a positive integer, n, new families, S and U, of binary sequences of period 2/sup n/-1 with low correlations are proposed, where for some positive integer, e, S is defined for odd n/e and U for even n/e. The family S has four-valued correlations and is a generalization of the family of Gold-like sequences introduced by S. Boztas and P.V. Kumar (see ibid., vol.40, p.532-7, 1994). The family U, which is also a generalization of the sequence family defined by P. Udaya ("Polyphase and frequency hopping sequences obtained from finite rings", Ph.D. dissertation, Dept. Elec. Eng., Indian Inst. Technol., Kanpur, 1992), has six-valued correlations. The relationship between Gold-like sequences and Gold sequences is the same as the relationship between the family S and the family constructed from the binary sequences partially contributed by R. Gold (see ibid., vol.IT-14, p.154-6, 1968), T. Kasami (see Coordinated Sci. Lab., Univ. of Illinois,Urbana-Champaign, Tech. Rep. R-285, AD 632574, 1966), and Welch. Using a lifting idea (No, J.-S. and Kumar, P.V., ibid., vol.35, p.371-9, 1989) for the families S and U, families of binary sequences with the same correlation distributions and large linear span are also constructed.