A generalized recursive construction for de Bruijn sequences

Games, Richard A.

doi:10.1109/tit.1983.1056764

Cited by 22 publications

(7 citation statements)

References 10 publications

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“…Suppose that the cycle of A is p(A) = q n , where n is a given natural number n 1 and A i = (a i , a i+1 , · · · , a i+n−1 ), i = 0, 1, · · · , q n − 1, which consists of all possible q n ordered sequences b 0 b 1 b 2 · · · b n−1 over the alphabet K(|K| = n). The cycle of q n letters is called a q-ary De Bruijn sequence of order n [12][13] . It contains each sub-string of length n exactly once.…”

Section: De Bruijn Sequence and Its Constructionmentioning

confidence: 99%

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Construction for M-arrays and application in structured light

Jia

Zhang

2011

J. Shanghai Univ.(Engl. Ed.)

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M-arrays are random arrays in which an appropriate sub-window appears only once in the whole array. Coded structured light based on M-arrays is one-shot technique to rapidly acquire 3D information of unknown surfaces by projecting suitable patterns onto a measuring surface. This paper presents a method to construct large size M-arrays based on the piece growing algorithm in which an array is constructed by many pieces through splicing each other. Reconstructing 3D shapes by utilizing the designed pattern based on constructed M-arrays for two objects are given.

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Section: De Bruijn Sequence and Its Constructionmentioning

confidence: 99%

“…The number of states in a cycle of G f (length of cycle) is called the period of the cycle, denoted by p. There is a correlation p q n between p and q n . The sequence with period q n is called the De Bruijn sequence [12][13] .…”

Section: De Bruijn Sequence and Its Constructionmentioning

confidence: 99%

Construction for M-arrays and application in structured light

Jia

Zhang

2011

J. Shanghai Univ.(Engl. Ed.)

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“…Other algorithms can be found in [21][22][23][24][25][26][27][28]. In [29], performances (in terms of time) of the algorithms from [20], [25], and [27] are empirically compared, and the last one is shown to have the best performance.…”

Section: Maximization Of the Number Of Different Subwordsmentioning

confidence: 99%

Test Sequence Construction Using Minimum Information on the Tested System

Kuliamin

2005

Program Comput Soft

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In the paper, approaches to constructing test sequences are considered in the case where only admissible input actions on the system are known, whereas no information about the states of the system or transitions between them in response to these actions is available. Two approaches to constructing test sequences that guarantee the widest variety of situations arising in the course of testing are suggested. The first approach gives rise to the so-called de Bruijn sequences. The second approach yields sequences covering all states or transitions in all finite automata with the number of states not exceeding a given constant. Both kinds of sequences are related to the combinatorial analysis of words in finite alphabets. Some methods for constructing such sequences are also discussed.

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“…All algorithms for constructing de Bruijn sequences (except for a class constructed from the m-sequences of period 2 n − 1) require a huge memory space. It is infeasible to construct a de Bruijn sequence or a nonlinear modified de Bruijn sequence with period 2 n when n > 30 [6], [7], [9]. (It is a well known fact that in design of secure systems, if one sequence can be obtained by removing or inserting one bit from another sequence, and the resulting sequence has a large linear span, then it is not considered as secure.…”

Section: Introductionmentioning

confidence: 99%

Elliptic Curve Pseudorandom Sequence Generators

Gong

Berson

Stinson

2000

Lecture Notes in Computer Science

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In this paper, we introduce a new approach to the generation of binary sequences by applying trace functions to elliptic curves over GF (2 m). We call these sequences elliptic curve pseudorandom sequences (EC-sequence). We determine their periods, distribution of zeros and ones, and linear spans for a class of EC-sequences generated from supersingular curves. We exhibit a class of EC-sequences which has half period as a lower bound for their linear spans. EC-sequences can be constructed algebraically and can be generated efficiently in software or hardware by the same methods that are used for implementation of elliptic curve public-key cryptosystems.

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A generalized recursive construction for de Bruijn sequences

Cited by 22 publications

References 10 publications

Construction for M-arrays and application in structured light

Construction for M-arrays and application in structured light

Test Sequence Construction Using Minimum Information on the Tested System

Elliptic Curve Pseudorandom Sequence Generators

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