Maximum length sequences (MLS) are a type of pseudorandom binary sequences with specific properties (see Wikipedia: Maximum length sequence, or m linear feedback shift register. Properties that hold include
- Window property: A sliding window of length m, passed along an m-sequence for 2m-1 positions, will span every possible m-bit number, except all zeros, once and only once. That is, every state of an m-bit state register will be encountered, with the exception of all zeros.
- Balance property: The number of "1"s in the sequence is one greater than the number of "0"s.
Is there a similar type of pseudorandom binary sequences known/constructible for which
- the "Window property" holds, but
- which are unbalanced, i.e. having p % ones and (100-p)% zeros ?