Lower bounds on the weight complexities of cascaded binary sequences
AUSCRYPT '90 Proceedings of the international conference on cryptology on Advances in cryptology
An algorithm for the k-error linear complexity of sequences over GF(pm) with period pn, p a prime
Information and Computation
Computation of the k-Error Linear Complexity of Binary Sequences with Period 2n
ASIAN '96 Proceedings of the Second Asian Computing Science Conference on Concurrency and Parallelism, Programming, Networking, and Security
Computing the error linear complexity spectrum of a binary sequence of period 2n
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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The linear Games-Chan algorithm for computing the linear complexity c(s) of a binary sequence s of period ℓ = 2n requires the knowledge of the full sequence, while the quadratic Berlekamp-Massey algorithm only requires knowledge of 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 analogues of the k-error linear complexity and of the error linear complexity spectrum for finite binary sequences viewed as initial segments of infinite sequences with period a power of two. Lauder and Paterson apply their algorithm to decoding binary repeated-root cyclic codes of length ℓ = 2n in ${\mathcal O}(\ell({\rm log}_{2}\ell)^2)$ time. We improve on their result, developing a decoding algorithm with ${\mathcal O}(\ell)$ bit complexity.