Quaternary Sequences over Galois Rings with Good Correlation Obtained from Modified Binary Sequences over Galois Fields

由伽罗瓦域上的修正二元序列得到的具有良好相关性的伽罗瓦环上的四元序列

• 批准号: 14550395
• 负责人: MORIUCHI Tsutomu
• 金额: $ 0.96万
• 依托单位: Yatsushiro National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14550395/
• 关键词: Quaternary Sequence; Pseudorandom Sequences; Gold Sequences; Gold-like Sequences; Spread Spectrum Communication; CDMA Communication; Sequences over Galois Rings; Kasami Sequences

This research proposed the new sets of quaternary sequences over Galois rings obtained from modified some well-known sets of binary sequences over Galois fields, and clarified its correlation distributions to compare with those of the binary ones.First, we constructed the sets of quaternary sequences over Galois rings modified from the sets of binary sequences over Galois fields such as Gold Sequences and Gold-like sequences. Secondly, the correlation distributions were analyzed involving numerical computations. These quaternary sequences are easily built by the binary sequences without its characteristic polynomials over Galois rings. The correlation distributions of the new sets were clarified to be similar to those of the binary sequences we used. The nontrivial maximum correlation value in the sequence sets is approximately equal to √<2N>, where N represents the period of a sequence, which is optimal asymptotically according to the Welch Lower Bound, and the family size equal to those of the binary sequence sets. Thus, the results show that the proposed sets of quaternary sequences were able to apply to spread spectrum CDMA.

本文通过对Galois域上一些著名的二元序列集的修改，得到了Galois环上的四元序列集，并阐明了其相关分布，与二元序列集的相关分布进行了比较。首先，我们从Galois域上的二元序列集（如Gold序列和Gold-like序列）出发，构造了Galois环上的四元序列集。其次，通过数值计算分析了相关分布。这类四元序列可由Galois环上的二元序列构造而成，而不需要其特征多项式。新集合的相关分布被澄清为与我们使用的二进制序列的相关分布相似。序列集合中的非平凡最大相关值近似等于N<2N>，其中N表示序列的周期，根据Welch下界，它是渐近最优的，族大小等于二元序列集合的族大小。因此，结果表明，所提出的四元序列集能够应用于扩频CDMA。

项目成果

S.Uehara, T.Moriuchi, K.Imamura: "GF(3)上のm-系列の相互相関におけるDobbertinの予想に関する考察"Proceedings of the 26^<th> Symposium on Information Theory and Its Applications(SITA 2003). SITA2003. 57-60 (2003)

S.Uehara、T.Moriuchi、K.Imamura：“关于 GF(3) 上 m 序列互相关中的 Dobbertin 猜想”第 26 届信息论及其应用研讨会论文集(SITA 2003) ) )。SITA2003。

T.Moriuchi, S.Uehara, K.Imamura: "Correlation Properties of Quaternary Sequences Obtained from the Binary Gold Sequences with Period 2^m-l, m Odd"Proceedings of the 25th Symposium, on Information Theory and Its Applications (SITA2002). Vol.II. 671-674 (20

T.Moriuchi、S.Uehara、K.Imamura：“从周期为 2^m-l，m Odd 的二元金序列获得的四元序列的相关性”第 25 届信息论及其应用研讨会论文集（SITA2002）。

T.Moriuchi, S.Uehara, K.Imamura: "Correlation Distribution of Quaternary Sequences Obtained from Modified Binary Gold-like Sequences"IEICE Research Meeting on Information Theory. IT2003-5. 11-15 (2003)

T.Moriuchi、S.Uehara、K.Imamura：“从修改的二元类金序列获得的四元序列的相关分布”IEICE 信息论研究会议。

T.Moriuchi, S.Uehara, K.Imamura: "Correlation Distribution of Quaternary Sequences Obtained from the Binary Gold Sequences"The 2003 IEEE International Symposium on Information Theory (ISIT 2003). ISIT2003. 380 (2003)

T.Moriuchi、S.Uehara、K.Imamura：“从二进制黄金序列获得的四元序列的相关分布”2003 年 IEEE 国际信息论研讨会 (ISIT 2003)。

T.Moriuchi, S.Uehara, K.Imamura: "Correlation Distribution of Quaternary Sequences Obtained from the Binary Gold Sequences"The 2003 IEEE International Symposium on Information Theory(ISIT 2003) on July 29-July 4,2003. ISIT2003. 380 (2003)

T.Moriuchi、S.Uehara、K.Imamura：“Correlation Distribution of Quaternary Sequences Getd from the Binary Gold Sequences”2003年IEEE国际信息论研讨会(ISIT 2003)，2003年7月29日至7月4日。