184 research outputs found
Corrigendum to New Generalized Cyclotomic Binary Sequences of Period
New generalized cyclotomic binary sequences of period are proposed in
this paper, where is an odd prime. The sequences are almost balanced and
their linear complexity is determined. The result shows that the proposed
sequences have very large linear complexity if is a non-Wieferich prime.Comment: In the appended corrigendum, we pointed out that the proof of Lemma 6
in the paper only holds for and gave a proof for any when
is a non-Wieferich prim
Linear complexity of generalized cyclotomic sequences of period
In this paper, we construct two generalized cyclotomic binary sequences of
period based on the generalized cyclotomy and compute their linear
complexity, showing that they are of high linear complexity when
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
The linear complexity of new binary cyclotomic sequences of period
In this paper, we determine the linear complexity of a class of new binary
cyclotomic sequences of period pn constructed by Z. Xiao et al. (Des. Codes
Cryptogr. DOI 10.1007/s10623-017-0408-7) and prove their conjecture about high
linear complexity of these sequences
Note about the linear complexity of new generalized cyclotomic binary sequences of period
This paper examines the linear complexity of new generalized cyclotomic
binary sequences of period recently proposed by Yi Ouang et al.
(arXiv:1808.08019v1 [cs.IT] 24 Aug 2018). We generalize results obtained by
them and discuss author's conjecture of this paper
Linear Complexity of Geometric Sequences Defined by Cyclotomic Classes and Balanced Binary Sequences Constructed by the Geometric Sequences
Pseudorandom number generators are required to generate pseudorandom numbers
which have good statistical properties as well as unpredictability in
cryptography. An m-sequence is a linear feedback shift register sequence with
maximal period over a finite field. M-sequences have good statistical
properties, however we must nonlinearize m-sequences for cryptographic
purposes. A geometric sequence is a sequence given by applying a nonlinear
feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a
geometric sequence whose nonlinear feedforward function is given by the
Legendre symbol, and showed the period, periodic autocorrelation and linear
complexity of the sequence. Furthermore, Nogami et al. proposed a
generalization of the sequence, and showed the period and periodic
autocorrelation. In this paper, we first investigate linear complexity of the
geometric sequences. In the case that the Chan--Games formula which describes
linear complexity of geometric sequences does not hold, we show the new formula
by considering the sequence of complement numbers, Hasse derivative and
cyclotomic classes. Under some conditions, we can ensure that the geometric
sequences have a large linear complexity from the results on linear complexity
of Sidel'nikov sequences. The geometric sequences have a long period and large
linear complexity under some conditions, however they do not have the balance
property. In order to construct sequences that have the balance property, we
propose interleaved sequences of the geometric sequence and its complement.
Furthermore, we show the periodic autocorrelation and linear complexity of the
proposed sequences. The proposed sequences have the balance property, and have
a large linear complexity if the geometric sequences have a large one.Comment: 20 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1709.0516
A further study on the linear complexity of new binary cyclotomic sequence of length
Recently, a conjecture on the linear complexity of a new class of generalized
cyclotomic binary sequences of period was proposed by Z. Xiao et al.
(Des. Codes Cryptogr., DOI 10.1007/s10623-017-0408-7). Later, for the case
being the form with , Vladimir Edemskiy proved the conjecture
(arXiv:1712.03947). In this paper, under the assumption of and , the conjecture
proposed by Z. Xiao et al. is proved for a general by using the Euler
quotient. Actually, a generic construction of -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
Linear complexity and trace representation of quaternary sequences over based on generalized cyclotomic classes modulo
We define a family of quaternary sequences over the residue class ring modulo
of length , a product of two distinct odd primes, using the generalized
cyclotomic classes modulo and calculate the discrete Fourier transform
(DFT) of the sequences. The DFT helps us to determine the exact values of
linear complexity and the trace representation of the sequences.Comment: 16 page
Linear complexity of generalized cyclotomic sequences of order 4 over F_l
Generalized cyclotomic sequences of period pq have several desirable
randomness properties if the two primes p and q are chosen properly. In
particular,Ding deduced the exact formulas for the autocorrelation and the
linear complexity of these sequences of order 2. In this paper, we consider the
generalized sequences of order 4. Under certain conditions, the linear
complexity of these sequences of order 4 is developed over a finite field F_l.
Results show that in many cases they have high linear complexity.Comment: Since there is a crucial error in Theorem 1 in the first version, we
replace it by the new on
Linear Complexity of Ding-Helleseth Generalized Cyclotomic Binary Sequences of Any Order
This paper gives the linear complexity of binary Ding-Helleseth generalized
cyclotomic sequences of any order
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