5 research outputs found
Constructions of Optimal and Near-Optimal Quasi-Complementary Sequence Sets from an Almost Difference Set
Compared with the perfect complementary sequence sets, quasi-complementary
sequence sets (QCSSs) can support more users to work in multicarrier CDMA
communications. A near-optimal periodic QCSS is constructed in this paper by
using an optimal quaternary sequence set and an almost difference set. With the
change of the values of parameters in the almost difference set, the
near-optimal QCSS can become asymptotically optimal and the number of users
supported by the subcarrier channels in CDMA system has an exponential growth
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
New Quadriphase Sequences families with Larger Linear Span and Size
In this paper, new families of quadriphase sequences with larger linear span
and size have been proposed and studied. In particular, a new family of
quadriphase sequences of period for a positive integer with an
even positive factor is presented, the cross-correlation function among
these sequences has been explicitly calculated. Another new family of
quadriphase sequences of period for a positive integer with
an even positive factor is also presented, a detailed analysis of the
cross-correlation function of proposed sequences has also been presented
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
Cyclic bent functions and their applications in codes, codebooks, designs, MUBs and sequences
Let be an even positive integer. A Boolean bent function on \GF{m-1}
\times \GF {} is called a \emph{cyclic bent function} if for any a\neq b\in
\GF {m-1} and \epsilon \in \GF{}, is
always bent, where x_1\in \GF {m-1}, x_2 \in \GF {}. Cyclic bent functions
look extremely rare. This paper focuses on cyclic bent functions on \GF {m-1}
\times \GF {} and their applications. The first objective of this paper is to
construct a new class of cyclic bent functions, which includes all known
constructions of cyclic bent functions as special cases. The second objective
is to use cyclic bent functions to construct good mutually unbiased bases
(MUBs), codebooks and sequence families. The third objective is to study cyclic
semi-bent functions and their applications. The fourth objective is to present
a family of binary codes containing the Kerdock code as a special case, and
describe their support designs. The results of this paper show that cyclic bent
functions and cyclic semi-bent functions have nice applications in several
fields such as symmetric cryptography, quantum physics, compressed sensing and
CDMA communication