Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A further study on the linear complexity of new binary cyclotomic
  sequence of length $p^r$   Recently, a conjecture on the linear complexity of a new class of generalized
cyclotomic binary sequences of period $p^r$ was proposed by Z. Xiao et al.
(Des. Codes Cryptogr., DOI 10.1007/s10623-017-0408-7). Later, for the case $f$
being the form $2^r$ with $r\ge 1$, Vladimir Edemskiy proved the conjecture
(arXiv:1712.03947). In this paper, under the assumption of $2^{p-1} \not\equiv
1 \bmod p^2$ and $\gcd(\frac{p-1}{{\rm {ord}}_{p}(2)},f)=1$, the conjecture
proposed by Z. Xiao et al. is proved for a general $f$ by using the Euler
quotient. Actually, a generic construction of $p^r$-periodic binary sequence
based on the generalized cyclotomy is introduced in this paper, which admits a
flexible support set and includes Xiao's construction as a special case, and
then an efficient method to compute the linear complexity of the sequence by
the generic construction is presented, based on which the conjecture proposed
by Z. Xiao et al. could be easily proved under the aforementioned assumption.

15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci