2 research outputs found
A lower bound on the 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of period
Let be an odd prime, a positive integer and a primitive root of
. Suppose
, , is
the generalized cyclotomic classes with . In this
paper, we prove that Gauss periods based on and are both equal to 0
for . As an application, we determine a lower bound on the 2-adic
complexity of a class of Ding-Helleseth generalized cyclotomic sequences of
period . The result shows that the 2-adic complexity is at least
, which is larger than , where is the
period of the sequence.Comment: 1
Asymptotically optimal codebooks derived from generalised bent functions
Codebooks are required to have small inner-product correlation in many
practical applications, such as direct spread code division multiple access
communications, space-time codes and compressed sensing. In general, it is
difficult to construct optimal codebooks. In this paper, two kinds of codebooks
are presented and proved to optimally optimal with respect to the welch bound.
Additionally, the constructed codebooks in this paper have new parameters