Lower bounds for the linear complexity of sequences over residue rings
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Binary sequences derived from ML-sequences over rings I: periods and minimal polynomials
Journal of Cryptology
Cryptoanalysis Based on 2-Adic Rational Approximation
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Fast Software Encryption, Cambridge Security Workshop
Autocorrelations of Maximum Period FCSR Sequences
SIAM Journal on Discrete Mathematics
Periodicity and distribution properties of combined FCSR sequences
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Arithmetic crosscorrelations of feedback with carry shift register sequences
IEEE Transactions on Information Theory
A lower bound on the linear span of an FCSR
IEEE Transactions on Information Theory
Partial period distribution of FCSR sequences
IEEE Transactions on Information Theory
Compression mappings on primitive sequences over Z/(pe)
IEEE Transactions on Information Theory
Uniqueness of the distribution of zeroes of primitive level sequences over Z/(pe)
Finite Fields and Their Applications
On the k-error linear complexity of l-sequences
Finite Fields and Their Applications
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A maximal length feedback with carry shift register sequence is also called an l-sequence. Although termwise exclusive ors of l-sequences are long thought to be a type of good pseudorandom sequences, few of their statistical properties have been proved yet. This paper completely determines the period of a termwise exclusive or of several l-sequences generated by FCSRs with distinct nonprime connection integers. The main result shows that either it attains the maximum or half of it and the associated sufficient conditions are also presented. Moreover, this periodicity property also holds for generalized l-sequences of the form {A@x^tmodp^emod2}"t"="0^~ where @x is a primitive root modulo odd prime number power p^e and A is an integer relatively prime to p.