Abstract:
This paper is concerned with the construction of de Bruijn sequences of spann--binary sequences of period2^{n}in which every binaryn-tuple appears as somenconsecutive ter...Show MoreMetadata
Abstract:
This paper is concerned with the construction of de Bruijn sequences of spann--binary sequences of period2^{n}in which every binaryn-tuple appears as somenconsecutive terms in one period of the sequence. Constructions in the literature are based on maximum length linear sequences, algorithms which start from scratch, and recursive methods which start with a single de Bruijn sequence of spannand produce one of spann+1. We give a more general recursive construction which takes two de Brnijn sequences of spannand produces a de Bruijn sequence of spann+1. In addition, for a special case of the construction, the complexity (shortest linear recursion that generates the sequence) of the resulting sequence is determined in terms of the complexities of the ingredient sequences. In particular, de Bruijn sequences of spann+1with maximum complexity2^{(n+1)}-1are obtained from maximum complexity sequences of spann. Reverse-complementary de Bruijn sequences are also considered.
Published in: IEEE Transactions on Information Theory ( Volume: 29, Issue: 6, November 1983)