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## Generating (n,2) De Bruijn Sequences with Some Balance and Uniformity Properties (2001)

### Citations

99 |
Applied and Algorithmic Graph Theory
- Chartrand, Oellermann
- 1993
(Show Context)
Citation Context ...ld theory or combinatorial theory to generate a single (n,m) de Bruijn sequence, but in addition, there is a well-known algorithm to sample, with equal probability, “random” (n,m) de Bruijn sequen=-=ces [1]-=-. An excellent survey has been provided by Fredricksen [3]. Owing to the special properties of de Bruijn sequences, there are various recent applications of (n,m) de Bruijn sequences, such as the plan... |

98 |
A survey of full length nonlinear shift register cycle algorithms
- Fredricksen
- 1982
(Show Context)
Citation Context ...of length m, s s s 1 2 ... , (1) i+ i+ i+ m is unique with subscripts in (1) taken modulo n m . For m≥2 and n≥2, there are 1 1 N=[ ( 1)! ] m − n m − n −m n− ⋅ n (n,m) de Bruijn sequences=-= (Fredricksen [3])-=-. For example, there are 36 pairs (i.e., m=2) which may be formed using n=6 symbols. The number of (6,2) de Bruijn sequences is over 3.87×10 15 . During the 70s-80s, de Bruijn sequences were well stu... |

52 |
Necklaces of Beads in k Colors and k-ary De Bruijn Sequences
- Fredricksen, Maiorana
- 1978
(Show Context)
Citation Context ...×10 15 . During the 70s-80s, de Bruijn sequences were well studied and several algorithms have been proposed for generating such sequences, e.g., Fredricksen and Kessler [4], Fredricksen and Maiorana=-= [5]-=-, and Ralston [10]. Most of those proposed algorithms use concepts of either finite field theory or combinatorial theory to generate a single (n,m) de Bruijn sequence, but in addition, there is a well... |

36 |
Generation of uniquely encoded light patterns for range data acquisition
- Griffin, Narasimhan, et al.
- 1992
(Show Context)
Citation Context ...e various recent applications of (n,m) de Bruijn sequences, such as the planning of reaction time experiments (Emerson and Tobias [2] and Sohn et al. [11]) and 3-D pattern recognition (Griffin et al. =-=[6]-=-, Hsieh [7-9], and Yee and Griffin [12]). Hsieh [8] describes some of these recent applications. In the reaction time experiment problems in which n stimuli are used and the effect of the preceding st... |

12 |
Lexicographic compositions and debruijn sequences
- Fredricksen, Kessler
- 1977
(Show Context)
Citation Context ... Bruijn sequences is over 3.87×10 15 . During the 70s-80s, de Bruijn sequences were well studied and several algorithms have been proposed for generating such sequences, e.g., Fredricksen and Kessler=-= [4]-=-, Fredricksen and Maiorana [5], and Ralston [10]. Most of those proposed algorithms use concepts of either finite field theory or combinatorial theory to generate a single (n,m) de Bruijn sequence, bu... |

9 |
A new memoryless algorithm for De Bruijn sequences
- Ralston
- 1981
(Show Context)
Citation Context ...he 70s-80s, de Bruijn sequences were well studied and several algorithms have been proposed for generating such sequences, e.g., Fredricksen and Kessler [4], Fredricksen and Maiorana [5], and Ralston =-=[10]-=-. Most of those proposed algorithms use concepts of either finite field theory or combinatorial theory to generate a single (n,m) de Bruijn sequence, but in addition, there is a well-known algorithm t... |

8 | Decoding structured light patterns for three-dimensional imaging systems - Hsieh - 2001 |

4 |
Computer program for quasi-random stimulus sequences with equal transition frequencies
- Emerson, Tobias
- 1995
(Show Context)
Citation Context ...travels the second circuit in G(n-2). Similarly, since for each row of matrix A, the cell with smaller L[i,j] (except zero) has higher priority to be assigned. This further implies that when the cell =-=[4,2] is assigned-=-, all cells A[i,j] (except for [2,n]), where [i,j]∈G(v), 2 v=1,2,…, n-2, have been assigned. Since 1 + ( Gn ( −2) − 1) + Gv () = n −2n, thus we have A[4,2]=n 2 −2n. Therefore, in Step 2, w... |

2 | Optimal sequences of trials for balancing practice and repetition effects
- Sohn, Bricker, et al.
- 1997
(Show Context)
Citation Context ...pecial properties of de Bruijn sequences, there are various recent applications of (n,m) de Bruijn sequences, such as the planning of reaction time experiments (Emerson and Tobias [2] and Sohn et al. =-=[11]-=-) and 3-D pattern recognition (Griffin et al. [6], Hsieh [7-9], and Yee and Griffin [12]). Hsieh [8] describes some of these recent applications. In the reaction time experiment problems in which n st... |

1 |
De Bruijn Sequences Generation
- Hsieh
(Show Context)
Citation Context ...quences, such as the planning of reaction time experiments (Emerson and Tobias [2] and Sohn et al. [11]) and 3-D pattern recognition (Griffin et al. [6], Hsieh [7-9], and Yee and Griffin [12]). Hsieh =-=[8]-=- describes some of these recent applications. In the reaction time experiment problems in which n stimuli are used and the effect of the preceding stimulus is considered, the (n,2) de Bruijn sequences... |

1 | Three-dimensional imaging system, Optical Engineering 33 - Yee, Griffin - 1994 |