A method for constructing decodable de Bruijn sequences

We present two related methods of construction for de Bruijn (1946) 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 within the sequence of any particular "window" can be found very simply. Sequences with simple decoding algorithms are of considerable practical importance in position location applications.

[1]  Fan Chung Graham,et al.  Universal cycles for combinatorial structures , 1992, Discret. Math..

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

[3]  Abraham Lempel,et al.  On a Homomorphism of the de Bruijn Graph and its Applications to the Design of Feedback Shift Registers , 1970, IEEE Transactions on Computers.

[4]  Tuvi Etzion,et al.  Constructions for perfect maps and pseudorandom arrays , 1988, IEEE Trans. Inf. Theory.

[5]  Kenneth G. Paterson,et al.  Decoding Perfect Maps , 1994, Des. Codes Cryptogr..

[6]  Chris J. Mitchell.  Constructingc-ary Perfect Factors , 1994, Des. Codes Cryptogr..

[7]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[8]  Chris J. Mitchell,et al.  Coding Schemes for Two-Dimensional Position Sensing , 1992 .

[9]  Ruey-Wen Liu,et al.  Equivalence of nonlinear shift-registers , 1964, IEEE Trans. Inf. Theory.

[10]  E. M. Petriu.  New pseudorandom/natural code conversion method , 1988 .

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

[12]  Kenneth G. Paterson,et al.  Storage efficient decoding for a class of binary be Bruijn sequences , 1995, Discret. Math..

[13]  Kenneth G. Paterson.  Perfect factors in the de Bruijn graph , 1995, Des. Codes Cryptogr..

[14]  H. Fredricksen.  A Survey of Full Length Nonlinear Shift Register Cycle Algorithms , 1982 .

[15]  Elwood S. Buffa,et al.  Graph Theory with Applications , 1977 .

[16]  Andrew M. Odlyzko,et al.  Discrete Logarithms in Finite Fields and Their Cryptographic Significance , 1985, EUROCRYPT.