New Results on the Imbalance of FCSR Sequences and LFSR Subsequences

Linear feedback shift registers (LFSRs) and feedback with carry shift registers (FCSRs) can be used in cryptography, communications and circuit testings. In 2014, Gu and Klapper investigated the imbalance properties of FCSR sequences and gave two bounds for the one symbol and two consecutive symbol cases, which were then improved in 2015. In 2016, the imbalance properties of LFSR subsequences were studied and an upper bound was deduced. In this paper, we revisit the imbalance properties of the above sequences and improve upon their bounds.