English

Linear complexity of quaternary sequences over Z_4 derived from generalized cyclotomic classes modulo 2p

Number Theory 2016-03-17 v1 Cryptography and Security

Abstract

We determine the exact values of the linear complexity of 2p-periodic quaternary sequences over Z_4 (the residue class ring modulo 4) defined from the generalized cyclotomic classes modulo 2p in terms of the theory of of Galois rings of characteristic 4, where p is an odd prime. Compared to the case of quaternary sequences over the finite field of order 4, it is more dificult and complicated to consider the roots of polynomials in Z_4[X] due to the zero divisors in Z_4 and hence brings some interesting twists. We answer an open problem proposed by Kim, Hong and Song.

Keywords

Cite

@article{arxiv.1603.05086,
  title  = {Linear complexity of quaternary sequences over Z_4 derived from generalized cyclotomic classes modulo 2p},
  author = {Zhixiong Chen and Vladimir Edemskiy},
  journal= {arXiv preprint arXiv:1603.05086},
  year   = {2016}
}
R2 v1 2026-06-22T13:12:16.549Z