Euclidean Modules and Multisequence Synthesis
Euclidean Modules and Multisequence Synthesis
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欧几里得模和多序列综合
DOI：
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发表时间：
2001
期刊：
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通讯作者：
Liping Wang
中科院分区：
文献类型：
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作者：
Liping Wang
本文将交换环中欧氏环的概念推广到任意模，给出一个特殊的欧氏Fq[x]-模Kn，其中Fq是有限域，n是正整数，K = Fq((x-1))。由此通过Fq[x]-格基约简算法推导出其中的广义欧氏算法。作为其直接应用，我们提出了一种新的多序列合成算法，与Feng-Tzeng的广义欧几里德合成算法完全等效。另外在单序列合成的情况下它也相当于Mills连分数算法。
In this paper we extend the concept of Euclidean ring in commutative rings to arbitrary modules and give a special Euclidean Fq[x]-module Kn, where Fq is a finite field, n a positive integer and K = Fq((x-1)). Thus a generalized Euclidean algorithm in it is deduced by means of Fq[x]-lattice basis reduction algorithm. As its direct application, we present a new multisequence synthesis algorithm completely equivalent to Feng-Tzeng' generalized Euclidean synthesis algorithm. In addition it is also equivalent to Mills continued fractions algorithm in the case of the single sequence synthesis.