9,340 research outputs found
A New Method to Compute the 2-adic Complexity of Binary Sequences
In this paper, a new method is presented to compute the 2-adic complexity of
pseudo-random sequences. With this method, the 2-adic complexities of all the
known sequences with ideal 2-level autocorrelation are uniformly determined.
Results show that their 2-adic complexities equal their periods. In other
words, their 2-adic complexities attain the maximum. Moreover, 2-adic
complexities of two classes of optimal autocorrelation sequences with period
, namely Legendre sequences and Ding-Helleseth-Lam sequences,
are investigated. Besides, this method also can be used to compute the linear
complexity of binary sequences regarded as sequences over other finite fields.Comment: 16 page
Some New Balanced and Almost Balanced Quaternary Sequences with Low Autocorrelation
Quaternary sequences of both even and odd period having low autocorrelation
are studied. We construct new families of balanced quaternary sequences of odd
period and low autocorrelation using cyclotomic classes of order eight, as well
as investigate the linear complexity of some known quaternary sequences of odd
period. We discuss a construction given by Chung et al. in "New Quaternary
Sequences with Even Period and Three-Valued Autocorrelation" [IEICE Trans.
Fundamentals Vol. E93-A, No. 1 (2010)] first by pointing out a slight
modification (thereby obtaining new families of balanced and almost balanced
quaternary sequences of even period and low autocorrelation), then by showing
that, in certain cases, this slight modification greatly simplifies the
construction given by Shen et al. in "New Families of Balanced Quaternary
Sequences of Even Period with Three-level Optimal Autocorrelation" [IEEE Comm.
Letters DOI10.1109/LCOMM.2017.26611750 (2017)]. We investigate the linear
complexity of these sequences as well
Linear Complexity and Autocorrelation of two Classes of New Interleaved Sequences of Period
The autocorrelation and the linear complexity of a key stream sequence in a
stream cipher are important cryptographic properties. Many sequences with these
good properties have interleaved structure, three classes of binary sequences
of period with optimal autocorrelation values have been constructed by
Tang and Gong based on interleaving certain kinds of sequences of period .
In this paper, we use the interleaving technique to construct a binary sequence
with the optimal autocorrelation of period , then we calculate its
autocorrelation values and its distribution, and give a lower bound of linear
complexity. Results show that these sequences have low autocorrelation and the
linear complexity satisfies the requirements of cryptography
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
Autocorrelation and Linear Complexity of Quaternary Sequences of Period 2p Based on Cyclotomic Classes of Order Four
We examine the linear complexity and the autocorrelation properties of new
quaternary cyclotomic sequences of period 2p. The sequences are constructed via
the cyclotomic classes of order four
A lower bound on the 2-adic complexity of modified Jacobi sequence
Let be distinct primes satisfying and let
, , be Whiteman's generalized cyclotomic classes with
. In this paper, we give the values of Gauss
periods based on the generalized cyclotomic sets
and
. As an application, we
determine a lower bound on the 2-adic complexity of modified Jacobi sequence.
Our result shows that the 2-adic complexity of modified Jacobi sequence is at
least with period . This indicates that the 2-adic complexity
of modified Jacobi sequence is large enough to resist the attack of the
rational approximation algorithm (RAA) for feedback with carry shift registers
(FCSRs).Comment: 13 pages. arXiv admin note: text overlap with arXiv:1702.00822,
arXiv:1701.0376
On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences
We determine the 2-adic complexity of the Ding-Helleseth-Martinsen (DHM)
binary sequences by using cyclotomic numbers of order four, "Gauss periods" and
"quadratic Gauss sum" on finite field and valued in
where is a prime number and is
the period of the DHM sequences.Comment: 16 page
Linear complexity of quaternary sequences over Z_4 derived from generalized cyclotomic classes modulo 2p
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
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
New Binary Sequences with Optimal Autocorrelation Magnitude
New binary sequences of period � � for even � � are found. These sequences can be described by a � interleaved structure. The new sequences are almost balanced and have four-valued autocorrelation, i.e., � � � ��, which is optimal with respect to autocorrelation magnitude. Complete autocorrelation distribution and exact linear complexity of the sequences are mathematically derived. From the simple implementation with a small number of shift registers and a connector, the sequences have a benefit of obtaining large linear complexity
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