Probability mass functions for de Bruijn weight classes

Order n de Bruijn sequences are the period 2ⁿ binary sequences from n-stage feedback shift registers. The de Bruijn sequences have good randomness and complexity properties. The number of de Bruijn sequences in a weight class of the order n generating functions is unknown for all but the smallest n. This method uses relationships between short cycles of progressively increasing lengths and their combinatorial impacts to provide high resolution estimates of the probability mass functions for the weight class distribution for order n de Bruijn sequences. The technique in this paper is applied to order 7 where results are available for comparison and used to estimate order 8 where results are currently computationally intractable