An algorithm for the k-error linear complexity of sequences over GF(pm) with period pn, p a prime
Information and Computation
Shift Register Sequences
The Software-Oriented Stream Cipher SSC2
FSE '00 Proceedings of the 7th International Workshop on Fast Software Encryption
Grain: a stream cipher for constrained environments
International Journal of Wireless and Mobile Computing
The weight distribution of some irreducible cyclic codes
IEEE Transactions on Information Theory
Computing the error linear complexity spectrum of a binary sequence of period 2n
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
We study the stability of m-sequences in the sense of determining the number of errors needed for decreasing the period of the sequences, as well as giving lower bounds on the k -error linear complexity of the sequences. For prime periods the results are straightforward so we concentrate on composite periods. We give exact results for the case when the period is reduced by a factor which is a Mersenne number and for the case when it is reduced by a prime p such that the order of 2 modulo p equals p −1. The general case is believed to be difficult due to its similarity to a well studied problem in coding theory. We also provide results about the relative frequencies of the different cases. We formulate a conjecture regarding the minimum number of errors needed for reducing the period at all. Finally we apply our results to the LFSR components of several well known stream ciphers.