  Certain applications require the use of signals that combine both the
capability to operate with low signal-to-noise ratios and the ability to
support multiple users without interference. In the case where many users have
very different signal-to-noise ratios, it is necessary to consider coding
schemes that can be used in a multi-user environment but with different noise
immunity levels. Traditional detection systems based on the correlation
function and coding sequences have significant limitations in satisfying both
objectives, since the cross-correlation between coded signals corresponding
with different users is linked to the use of the same coded sequences length.
The research topic of binary sequences that have null cross-correlation and
different length has not been studied in depth, but it has potential
applications in multi-user environments. In this work an algorithm to generate
binary sequences completely uncorrelated with certain sets of complementary
sequences is presented. The proposed algorithm is based on nested Barker
sequences, and it is compared with a previous proposal based on an iterative
algorithm. This approach allows to generate more diversity of sequences of
different length than the iterative approach, which it makes useful for
applications based on binary sequences detection and expand the horizon of many
applications.
