Remarks on the generalized cyclotomic sequences of length $$2p^{m}$$

Abstract

This paper presents some nonrandom distribution properties of two generalized cyclotomic binary sequences of length \(2p^{m}\) constructed by Zhang et al. (Appl Algebra Eng Commun Comput 21:93–108, 2010). Using these properties we further study the \(k\)-error linear complexity and autocorrelation of these sequences. For some small values of \(k\), the upper bounds on the \(k\)-error linear complexity are derived, which are far less than their linear complexity. Finally the bounds on the autocorrelation of these sequences are also presented. Our results show that there exist some drawbacks in application of these two sequences.