Finite fields
Exploiting Multiples of the Connection Polynomial in Word-Oriented Stream Ciphers
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Generalized Joint Linear Complexity of Linear Recurring Multisequences
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Sequences with almost perfect linear complexity profile
EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
The minimal polynomial over Fq of linear recurring sequence over Fqm
Finite Fields and Their Applications
On minimal polynomials over Fqm and over Fq of a finite-length sequence over F qm
Finite Fields and Their Applications
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Since the F"q-linear spaces F"q^m and F"q"^"m are isomorphic, an m-fold multisequence S over the finite field F"q with a given characteristic polynomial f@?F"q[x], can be identified with a single sequence S over F"q"^"m with characteristic polynomial f. The linear complexity of S, which will be called the generalized joint linear complexity of S, can be significantly smaller than the conventional joint linear complexity of S. We determine the expected value and the variance of the generalized joint linear complexity of a random m-fold multisequence S with given minimal polynomial. The result on the expected value generalizes a previous result on periodic m-fold multisequences. Moreover we determine the expected drop of linear complexity of a random m-fold multisequence with given characteristic polynomial f, when one switches from conventional joint linear complexity to generalized joint linear complexity.