I. Introduction
The linear complexity and the -error linear complexity of periodic sequences over finite fields are important randomness measures for pseudorandom sequence generators employed in stream ciphers (see [10], [15], [30], [34], and [37]). If a sequence has low linear complexity, then it is vulnerable to cryptanalytic attacks based on the Berlekamp-Massey algorithm [23]. Moreover, cryptographically strong sequences should also have large linear complexity under small perturbations. This leads to the concept of the -error linear complexity [8], [10], [13], [36].