A de Bruijn sequence is a circular binary string of length 2 n that contains each binary string of length n exactly once as a substring. A maximum-density de Bruijn sequence is a circular binary string of length that contains each binary string of length n with density (number of 1s) between 0 and m, inclusively. In this paper we efficiently generate maximum-density de Bruijn sequences for all values of n and m. An interesting special case occurs when n = 2m + 1. In this case our result is a "complement-free de Bruijn sequence" since it is a circular binary string of length 2 n - 1 that contains each binary string of length n or its complement exactly once as a substring. © 2011 Springer-Verlag.
CITATION STYLE
Sawada, J., Stevens, B., & Williams, A. (2011). De Bruijn sequences for the binary strings with maximum density. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6552 LNCS, pp. 182–190). https://doi.org/10.1007/978-3-642-19094-0_19
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