Properties of the error linear complexity spectrum
IEEE Transactions on Information Theory
New results on periodic sequences with large k-error linear complexity
IEEE Transactions on Information Theory
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
The characterization of 2n-periodic binary sequences with fixed 1-error linear complexity
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Computing the linear complexity for sequences with characteristic polynomial fv
Cryptography and Communications
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The linear Games-Chan algorithm for computing the linear complexity c(s) of a binary sequence s of period lscr=2n requires the knowledge of the full sequence, while the quadratic Berlekamp-Massey algorithm requires knowledge of only 2c(s) terms. We show that we can modify the Games-Chan algorithm so that it computes the complexity in linear time knowing only 2c(s) terms. The algorithms of Stamp-Martin and Lauder-Paterson can also be modified, without loss of efficiency, to compute analogs of the k-error linear complexity for finite binary sequences viewed as initial segments of infinite sequences with period a power of two. We also develop an algorithm which, given a constant c and an infinite binary sequence s with period lscr=2n , computes the minimum number k of errors (and an associated error sequence) needed over a period of s for bringing the linear complexity of s below c. The algorithm has a time and space bit complexity of O(lscr). We apply our algorithm to decoding and encoding binary repeated-root cyclic codes of length lscr in linear, O(lscr), time and space. A previous decoding algorithm proposed by Lauder and Paterson has O(lscr(loglscr)2) complexity