Chapter

Sequences and Their Applications – SETA 2010

Volume 6338 of the series Lecture Notes in Computer Science pp 125-138

A General Approach to Construction and Determination of the Linear Complexity of Sequences Based on Cosets

  • Ayça ÇeşmelioğluAffiliated withFaculty of Engineering and Natural Sciences, Sabancı University
  • , Wilfried MeidlAffiliated withFaculty of Engineering and Natural Sciences, Sabancı University

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Abstract

We give a general approach to N-periodic sequences over a finite field \(\mathbb F_q\) constructed via a subgroup D of the group of invertible elements modulo N. Well known examples are Legendre sequences or the two-prime generator. For some generalizations of sequences considered in the literature and for some new examples of sequence constructions we determine the linear complexity.