Remarks on the k-error linear complexity of pn-periodic sequences
Designs, Codes and Cryptography
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'10 Proceedings of the 6th international conference on Sequences and their applications
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
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
On the stability of m-sequences
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
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Binary sequences with high linear complexity are of interest in cryptography. The linear complexity should remain high even when a small number of changes are made to the sequence. The error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed. We present an algorithm which computes the error linear complexity for binary sequences of period ℓ=2n using O(ℓ(logℓ)2) bit operations. The algorithm generalizes both the Games-Chan (1983) and Stamp-Martin (1993) algorithms, which compute the linear complexity and the k-error linear complexity of a binary sequence of period ℓ=2n, respectively. We also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of Reed-Muller codes.