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The behaviour of nonlinear turbo codes that use nonlinear finite state sequential machines (FSSMs), designed over the finite field GF(4), as constituent encoders is studied. These FSSMs show a nonzero output for the all-zero input case. The state-transitions structure and the randomness of the output for the all-zero input response of these FSSMs are studied for different initial state conditions. A relationship is found between these two characteristics and the BER performance or, equivalently, the form of the extrinsic information transfer chart of the corresponding turbo code. It is found that FSSMs with responses of the form of long closed cycles, and good randomness properties of the corresponding output are the best options as constituent encoders of nonlinear turbo codes designed over GF(4). A coefficient called the random behaviour coefficient is defined, to provide a quantitative measure of the behaviour of these FSSMs as constituent encoders of a turbo code.