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De Bruijn Sequences Revisited
"... A (noncircular) de Bruijn sequence w of order n is a word such that every word of length n appears exactly once in w as a factor. In this paper, we generalize the concept to different settings: the multishift de Bruijn sequence and the pseudo de Bruijn sequence. An mshift de Bruijn sequence of or ..."
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A (noncircular) de Bruijn sequence w of order n is a word such that every word of length n appears exactly once in w as a factor. In this paper, we generalize the concept to different settings: the multishift de Bruijn sequence and the pseudo de Bruijn sequence. An mshift de Bruijn sequence
Enumerating De Bruijn sequences
 MATCH Communications in Mathematical and in Computer Chemistry
"... A cycle is a sequence taken in a circular order—that is, follows, and are all the same cycle as. Given natural numbers and, a cycle of letters is called a complete cycle [1, 2], or De Bruijn sequence, if subsequences consist of all possible ordered sequences over the alphabet. In 1946, De Bruijn pro ..."
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A cycle is a sequence taken in a circular order—that is, follows, and are all the same cycle as. Given natural numbers and, a cycle of letters is called a complete cycle [1, 2], or De Bruijn sequence, if subsequences consist of all possible ordered sequences over the alphabet. In 1946, De Bruijn
Constructing Orthogonal de Bruijn Sequences
 LNCS 6844
, 2011
"... Abstract. A(σ, k)de Bruijn sequence is a minimum length string on an alphabet set of size σ which contains all σ k kmers exactly once. Motivated by an application in synthetic biology, we say a given collection of de Bruijn sequences are orthogonal if no two of them contain the same (k + 1)mer; t ..."
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Abstract. A(σ, k)de Bruijn sequence is a minimum length string on an alphabet set of size σ which contains all σ k kmers exactly once. Motivated by an application in synthetic biology, we say a given collection of de Bruijn sequences are orthogonal if no two of them contain the same (k + 1)mer
Evolutionary Construction of de Bruijn Sequences ∗
"... Abstract. A binary de Bruijn sequence of order n is a cyclic sequence of period 2 n, in which each nbit pattern appears exactly once. These sequences are commonly used in random number generation and symmetric keycryptographyparticularly in stream cipher design, mainly due to their good statistical ..."
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Abstract. A binary de Bruijn sequence of order n is a cyclic sequence of period 2 n, in which each nbit pattern appears exactly once. These sequences are commonly used in random number generation and symmetric keycryptographyparticularly in stream cipher design, mainly due to their good
FIXEDDENSITY DE BRUIJN SEQUENCES ∗
"... Abstract. De Bruijn sequences are circular strings of length 2 n whose substrings are the binary strings of length n. Our focus is on de Bruijn sequences for binary strings that have the same density (number of 1s). We construct circular strings of length ( n−1) ( n−1) + whose substrings of length ..."
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Abstract. De Bruijn sequences are circular strings of length 2 n whose substrings are the binary strings of length n. Our focus is on de Bruijn sequences for binary strings that have the same density (number of 1s). We construct circular strings of length ( n−1) ( n−1) + whose substrings of length
Enumerating Order 7 de Bruijn Sequences
"... Abstract—Order n de Bruijn sequences are the period 2 n binary sequences from nstage feedback shift registers. The de Bruijn sequences have randomness properties that are useful in data link security. Many de Bruijn sequences have nearly ideal twolevel autocorrelation properties necessary for sign ..."
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Abstract—Order n de Bruijn sequences are the period 2 n binary sequences from nstage feedback shift registers. The de Bruijn sequences have randomness properties that are useful in data link security. Many de Bruijn sequences have nearly ideal twolevel autocorrelation properties necessary
Construction for de Bruijn Sequences with Large Orders ∗
"... Sequences generated by maximumperiod nonlinear feedback shift registers are known as de Bruijn sequences. The problem of designing de Bruijn sequences has received considerable attention. There is only one full cycle in the state graph of de Bruijn sequences. Most popular algorithms for generatin ..."
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Sequences generated by maximumperiod nonlinear feedback shift registers are known as de Bruijn sequences. The problem of designing de Bruijn sequences has received considerable attention. There is only one full cycle in the state graph of de Bruijn sequences. Most popular algo
Cryptographically Strong de Bruijn Sequences with Large Periods
, 2012
"... In this paper we first refine Mykkeltveit et al.’s technique for producing de Bruijn sequences through compositions. We then conduct an analysis on an approximation of the feedback functions that generate de Bruijn sequences. The cycle structures of the approximated feedback functions and the linea ..."
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In this paper we first refine Mykkeltveit et al.’s technique for producing de Bruijn sequences through compositions. We then conduct an analysis on an approximation of the feedback functions that generate de Bruijn sequences. The cycle structures of the approximated feedback functions
Construction of de Bruijn Sequences of Minimal Complexity
, 1984
"... this paper we demonstrate that for each n >_ 3 there exists a de Bruijn sequence S of length 2" with C(S) = 2 nt + n, thus proving the conjecture by Chan et al ..."
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Cited by 9 (0 self)
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this paper we demonstrate that for each n >_ 3 there exists a de Bruijn sequence S of length 2" with C(S) = 2 nt + n, thus proving the conjecture by Chan et al
A Method for Constructing Decodable de Bruijn Sequences
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1996
"... In this paper we present two related methods of construction for de Bruijn sequences, both based on interleaving "smaller" de Bruijn sequences. Sequences obtained using these construction methods have the advantage that they can be "decoded" very efficiently, i.e., the position w ..."
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Cited by 7 (1 self)
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In this paper we present two related methods of construction for de Bruijn sequences, both based on interleaving "smaller" de Bruijn sequences. Sequences obtained using these construction methods have the advantage that they can be "decoded" very efficiently, i.e., the position
Results 1  10
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