In this paper, we present quasi-chaotic (QC) schemes for secure digital communication systems, designed over Galois fields (GFs) with optimal randomness properties. Schemes with the maximum-output sequence length (all-zero input response) are presented for different GFs. Two coefficients are used to quantitatively measure the proximity of the behavior of these schemes with respect to the ideal white noise behavior. The proposed schemes outperform those presented by Frey in his paper, and achieve the optimal QC properties available for a given chaotic digital scheme. The proposed schemes have also a very little loss in bit-error rate performance so that they are a good alternative to the design of systems for which encryption and error correction are important joint goals. They can be implemented with time-variant coefficients in order to highly improve the cryptographic properties of the transmission.