A Note on Sequences with the Shift and Add Property
Designs, Codes and Cryptography
Algebraic feedback shift registers
Theoretical Computer Science - Special issue: cryptography
Shift Register Sequences
Register Synthesis for Algebraic Feedback Shift Registers Based on Non-Primes
Designs, Codes and Cryptography
Distributional properties of d-FCSR sequences
Journal of Complexity - Special issue on coding and cryptography
Periodicity and Correlation Properties of d-FCSR Sequences
Designs, Codes and Cryptography
Decoding of codes defined by a single point on a curve
IEEE Transactions on Information Theory - Part 1
Generalized Berlekamp-Massey decoding of algebraic-geometric codes up to half the Feng-Rao bound
IEEE Transactions on Information Theory - Part 1
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We study algebraic feedback shift registers (AFSRs) based on quotients of polynomial rings in several variables over a finite field. These registers are natural generalizations of linear feedback shift registers. We describe conditions under which such AFSRs produce sequences with various ideal randomness properties. We also show that there is an efficient algorithm which, given a prefix of a sequence, synthesizes a minimal such AFSR that outputs the sequence.