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theorem
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In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
      
If the additive group of complex numbers acts algebraically on a normal affine variety, then the associated ring of invariants need not be finitely generated, but is an ideal transform of some normal affine algebra (Theorem 1).
      
If the variety is a complex affine space and the ring of invariants is isomorphic to a polynomial ring, then the action is conjugate to a translation (Theorem 3).
      
On the other hand, there is a locally trivialGa-action on a normal affine variety with nonfinitely generated ring of invariants (Theorem 2).
      
As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.
      
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Let Cp(x) denote the cyclic code generated by p(X), and Cpn(x) the principal ideal generated by p(X) in the algebra of polynomials modulo Xn - 1. The following theorems may make clear the idea behind the design of Fire codes.Theorem Ⅰ. If n is the length of Cp(x)q(x), and p(X) is relatively prime to q(X), then Cp(X)q(x) is equal to the intersection Cpn(x)Cqn(x).Theorem Ⅱ. Consider three cyclic codes with the intersection of the first two equal to the third. The syndromes of the two distinct...

Let Cp(x) denote the cyclic code generated by p(X), and Cpn(x) the principal ideal generated by p(X) in the algebra of polynomials modulo Xn - 1. The following theorems may make clear the idea behind the design of Fire codes.Theorem Ⅰ. If n is the length of Cp(x)q(x), and p(X) is relatively prime to q(X), then Cp(X)q(x) is equal to the intersection Cpn(x)Cqn(x).Theorem Ⅱ. Consider three cyclic codes with the intersection of the first two equal to the third. The syndromes of the two distinct bursts with respect to the first or second code are not the same if and only if the syndromes with respect to the third are not the same.

文中运用循环码求交运算的方法,对纠突发错误循环码的设计思想作了一些探讨,给出了Fire码的一种纠突发错误算法。

By assuming engineering approximation and using theorem[1] for orthogonal expansion of D(Fn⊕CLm), which is the D-transform of Fn⊕CLm, general expressions of normalized autocorrelation function and normalized power spectral density function of Fn⊕CLm have been derived, where Fn⊕CLm is the digital modulation of the combined code by a square wave with a frequency M times that of the clock frequency. Engineering design examples have also been given.

本文应用文献〔1〕所述的复码D变换正交展开定理,在工程近似假设的前提下,导出了复码数字调制在m倍钟频方波上的归一化自相关函数和功率谱密度函数的通用表达式,给出了工程设计实例。

In this paper two methods of high-speed decoding of Fire codes for disc error-correction are presented.Method I. For determination of erroneous address, high-speed backward shift circuits are used to perform the cyclic shift of P(x). The maximum number of times of shifting operation for the decoding with a code length N is less than (c + N/C). The erroneous address will directly be given by the counter.Method II. On the basis of Chinese remainder theorem, the erroneous address will directly be given by...

In this paper two methods of high-speed decoding of Fire codes for disc error-correction are presented.Method I. For determination of erroneous address, high-speed backward shift circuits are used to perform the cyclic shift of P(x). The maximum number of times of shifting operation for the decoding with a code length N is less than (c + N/C). The erroneous address will directly be given by the counter.Method II. On the basis of Chinese remainder theorem, the erroneous address will directly be given by the counter when P(x) and C are properly chosen. The maximum number of times of decoding shift is less than (e + c).Both methods are suitable for high-speed decoding in the disc storage system where arithmetic operation functions are not available and the zerofilling operation is not necessary. It is also suitable for arbitrary code length.

本文介绍磁盘纠错用法尔码的两种快速译码方法。 方法Ⅰ:在确定错误地址时,P(x)电路的循环移位采用快速反向移位电路,码长为N的最大译码移位操作次数小于(C+N/C)次,错误地址直接由计数器得到。 方法Ⅱ:根据孙子定理并加简化和推广应用,在适当选择P(x)和C后,错误地址直接由计数器得到。最大译码移位次数小于(e+C)次。 两者适用于不具备算术运算功能的磁盘存储器系统的快速译码,不需要补0操作,适用于随机码长。

 
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