A large class of nonlinear shift register sequences (Corresp.)

Hemmati, F.

doi:10.1109/tit.1982.1056469

Cited by 14 publications

(4 citation statements)

References 7 publications

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“…The adjacency graphs of LFSRs with characteristic polynomial (1 + x) m p(x) for m = 1, 2, 3 were studied in [8,11,16] respectively. But there are no results for m ≥ 4.…”

Section: The Adjacency Graphs Of Fsr((1 + X) 4 P(x)) and Fsr((1 + X) mentioning

confidence: 99%

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The adjacency graphs of some feedback shift registers

Jiang

Lin

2016

Des. Codes Cryptogr.

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In this paper, we consider the adjacency graphs of some feedback shift registers (FSRs), namely, the FSRs with characteristic functions of the form g = (x 0 + x 1 ) * f . Firstly, we give some properties about these FSRs. We prove that these FSRs generate only prime cycles, and these cycles can be divided into two sets such that each set contains no adjacent cycles. When f is a linear function, more properties about these FSRs are derived. For example, it is shown that, when f contains an odd number of terms, the adjacency graph of FSR((x 0 + x 1 ) * f ) can be determined directly from the adjacency graph of FSR( f ). Then, as an application of these results, we continue the work of Li et al. (IEEE Trans Inf Theory 60(5):3052-3061, 2014) to determine the adjacency graphs of FSR((1 + x) 4 p(x)) and FSR((1 + x) 5 p(x)), where p(x) is a primitive polynomial, and construct a large class of De Bruijn sequences from them.

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“…The adjacency graphs of LFSRs with characteristic polynomial (1 + x) m p(x) for m = 1, 2, 3 were studied in [8,11,16] respectively. But there are no results for m ≥ 4.…”

Section: The Adjacency Graphs Of Fsr((1 + X) 4 P(x)) and Fsr((1 + X) mentioning

confidence: 99%

“…. , k, are primitive polynomials and m is a positive integer <4 [8,[11][12][13]16]. By considering the conjugate pairs in a De Bruijn cycle, Mykkeltveit and Szmidt proved that an arbitrary De Bruijn cycle can be obtained by applying cross-join pair operations to a given one [15].…”

Section: Introductionmentioning

confidence: 99%

The adjacency graphs of some feedback shift registers

Jiang

Lin

2016

Des. Codes Cryptogr.

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show abstract

“…A de Biruijn graph [5] reproduces the state transition diagram of a cyclic code, taking as state identifier the content of the shift register memory elements used to produce the code word. As shown in [6] any code word produces; a closed path in the state diagram, starting from state 0, that is a state characterized by all null coordinates, and coming back to the same state after n steps, being n the code length.…”

Section: Decoding Methodsmentioning

confidence: 99%

“…The aim of the present paper is to introduce another decoding technique, which is based on the description of cyclic block codes by means of de Bruijn graphs [5]. A de Bruijn graph reproduces the state transition diagram of a cyclic code, taking as state identifier the content of the shift register memory elements used to produce the code word.…”

Section: Introductionmentioning

confidence: 99%