Minimal Polynomials of the Modified de Bruijn Sequences

It is well known that a de Bruijn sequence over F2 has the minimal polynomial (x + 1)d , where 2n−1 + n d 2n − 1. We study the minimal polynomials of the modified de Bruijn sequences. © 2007 Elsevier B.V. All rights reserved.

[1]  K. Williams,et al.  Gauss and Jacobi sums , 2021, Mathematical Surveys and Monographs.

[2]  Solomon W. Golomb,et al.  Linear spans of modified de Bruijn sequences , 1990, IEEE Trans. Inf. Theory.

[3]  Richard A. Games.  There Are No De Bruijn Sequences of Span n with Complexity 2n-1+n+1 , 1983, J. Comb. Theory, Ser. A.

[4]  K. Conrad,et al.  Finite Fields , 2018, Series and Products in the Development of Mathematics.

[5]  Solomon W. Golomb,et al.  Shift Register Sequences , 1981 .

[6]  Tuvi Etzion,et al.  Linear Complexity of de Brujin Sequences - Old and New Results , 1999, IEEE Trans. Inf. Theory.

[7]  Tuvi Etzion,et al.  Construction of de Bruijn sequences of minimal complexity , 1984, IEEE Trans. Inf. Theory.

[8]  Simon R. Blackburn.  A Note on Sequences with the Shift and Add Property , 1996, Des. Codes Cryptogr..

[9]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[10]  de Ng Dick Bruijn.  A combinatorial problem , 1946 .

[11]  Richard A. Games,et al.  On the Complexities of de Bruijn Sequences , 1982, J. Comb. Theory, Ser. A.

[12]  Rudolf Lide,et al.  Finite fields , 1983 .