Primitive polynomials,singer cycles and word-oriented linear feedback shift registers

Sudhir R.Ghorpade; Sartaj Ul Hasan; Meena Kumari

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Primitive polynomials,singer cycles and word-oriented linear feedback shift registers

机译：原始多项式，歌手周期和面向单词的线性反馈移位寄存器

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Using the structure of Singer cycles in general linear groups,we prove that a conjecture of Zeng et al.(Word-Oriented Feedback Shift Register:σ-LFSR, 2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive σ-LFSRs of a given order over a finite field,and it generalizes a known formula for the number of primitive LFSRs, which, in turn, is the number of primitive polynomials of a given degree over a finite field. Moreover, this conjecture is intimately related to an open question of Niederreiter (Finite Fields Appl 1:3-30,1995) on the enumeration of splitting subspaces of a given dimension.

机译：利用一般线性群中Singer循环的结构，我们证明了Zeng等人的猜想（Word-Oriented Feedback Shift Register：σ-LFSR，2007）在特殊情况下是肯定的，并概述了一种可行的方法在一般情况下证明这一点。这个猜想是关于有限域上给定阶数的本原σ-LFSR的数目，并且它概括了一个原始LFSR数的已知公式，这又是一个给定度数上a的原始多项式的数目。有限域。而且，这个猜想与Niederreiter的公开问题（Finite Fields Appl 1：3-30,1995）密切相关，该问题涉及给定维的分裂子空间的枚举。

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来源
《Designs, Codes and Crytography》 |2011年第2期|p.123-134|共12页
作者
Sudhir R.Ghorpade; Sartaj Ul Hasan; Meena Kumari;
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作者单位

Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India;

Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India,Scientific Analysis Group, Defense Research and Development Organisation, Metcalfe House, Delhi 110054, India;

Scientific Analysis Group, Defense Research and Development Organisation, Metcalfe House, Delhi 110054, India;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
primitive polynomial; linear feedback shift register (lfsr); primitive recursive vector sequence; singer cycle; singer subgroup; splitting subspaces;

机译：原始多项式;线性反馈移位寄存器（lfsr）;原始递归向量序列;歌手周期;歌手子群;分解子空间;

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7. Primitive polynomials, singer cycles and word-oriented linear feedback shift registers [O] . Sudhir R. Ghorpade, Sartaj Ul Hasan, Meena Kumari 2011

机译：原始多项式，歌手周期和面向字的线性反馈移位寄存器

Primitive polynomials,singer cycles and word-oriented linear feedback shift registers

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