47 research outputs found
Linear Complexity of A Family of Binary pq2 -periodic Sequences From Euler Quotients
We first introduce a family of binary -periodic sequences based on the Euler quotients modulo , where and are two distinct odd primes and divides . The minimal polynomials and linear complexities are determined for the proposed sequences provided that . The results show that the proposed sequences have high linear complexities
Artin's primitive root conjecture -a survey -
This is an expanded version of a write-up of a talk given in the fall of 2000
in Oberwolfach. A large part of it is intended to be understandable by
non-number theorists with a mathematical background. The talk covered some of
the history, results and ideas connected with Artin's celebrated primitive root
conjecture dating from 1927. In the update several new results established
after 2000 are also discussed.Comment: 87 pages, 512 references, to appear in Integer
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Finite Fields: Theory and Applications
Finite ļ¬elds are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of ļ¬nite ļ¬eld techniques in cryptography, error correcting codes, and random number generation