5阶分环数/ F/ p//sup n/

Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. Pub Date : 2005-10-31 DOI:10.1109/ISIT.2005.1523688

Jung-Soo Chung, Young-Sik Kim, Tae-Hyung Lim, Jong-Seon No, Habong Chung

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引用次数: 0

摘要

在本文中，我们利用著名的Fp上的五次Jacobi和的结果(b.c.b Berndt, et al.， 1998)，导出了扩展域Fp n上5阶的环切数。pne 1国防部5,我们获得的简单的封闭表达式分圆的数量的订单5 / Fp n。p 1国防部5枚,我们表达的割圆数量订购5 / F p n的丢番图系统的解决方案,需要评估分圆的数量的订单5 / Fp n。使用分圆的数量的订单5 / Fp n,自相关分布5-ary Sidel 'nikov pn - 1序列也派生

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Cyclotomic numbers of order 5 over F/sub p//sup n/

In this paper, we derive the cyclotomic numbers of order 5 over an extension field F_p ⁿ using the well-known results of quintic Jacobi sums over F_p (B. C. Berndt, et al., 1998). For p ne 1 mod 5, we have obtained the simple closed-form expression of the cyclotomic numbers of order 5 over F_p ⁿ. For p equiv 1 mod 5, we express the cyclotomic number of order 5 over F _p ⁿ in terms of the solution of the diophantine system which is required to evaluate the cyclotomic number of order 5 over F_p ⁿ. Using the cyclotomic numbers of order 5 over F_p ⁿ, autocorrelation distributions of 5-ary Sidel'nikov sequences of period pⁿ - 1 are also derived

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Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.

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