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Certain applications require the use of signals that combine both thecapability to operate with low signal-to-noise ratios and the ability tosupport multiple users without interference. In the case where many users havevery different signal-to-noise ratios, it is necessary to consider codingschemes that can be used in a multi-user environment but with different noiseimmunity levels. Traditional detection systems based on the correlationfunction and coding sequences have significant limitations in satisfying bothobjectives, since the cross-correlation between coded signals correspondingwith different users is linked to the use of the same coded sequences length.The research topic of binary sequences that have null cross-correlation anddifferent length has not been studied in depth, but it has potentialapplications in multi-user environments. In this work an algorithm to generatebinary sequences completely uncorrelated with certain sets of complementarysequences is presented. The proposed algorithm is based on nested Barkersequences, and it is compared with a previous proposal based on an iterativealgorithm. This approach allows to generate more diversity of sequences ofdifferent length than the iterative approach, which it makes useful forapplications based on binary sequences detection and expand the horizon of manyapplications.

Uncorrelated binary sequences of lengths 2a3b4c5d7e11f13g based on nested Barker codes and complementary sequences