641 research outputs found
A method for high precision reconstruction of air shower Xmax using two-dimensional radio intensity profiles
The mass composition of cosmic rays contains important clues about their
origin. Accurate measurements are needed to resolve long-standing issues such
as the transition from Galactic to extragalactic origin, and the nature of the
cutoff observed at the highest energies. Composition can be studied by
measuring the atmospheric depth of the shower maximum Xmax of air showers
generated by high-energy cosmic rays hitting the Earth's atmosphere. We present
a new method to reconstruct Xmax based on radio measurements. The radio
emission mechanism of air showers is a complex process that creates an
asymmetric intensity pattern on the ground. The shape of this pattern strongly
depends on the longitudinal development of the shower. We reconstruct Xmax by
fitting two-dimensional intensity profiles, simulated with CoREAS, to data from
the LOFAR radio telescope. In the dense LOFAR core, air showers are detected by
hundreds of antennas simultaneously. The simulations fit the data very well,
indicating that the radiation mechanism is now well-understood. The typical
uncertainty on the reconstruction of Xmax for LOFAR showers is 17 g/cm^2.Comment: 12 pages, 10 figures, submitted to Phys. Rev.
On the Construction of Near-MDS Matrices
The optimal branch number of MDS matrices makes them a preferred choice for
designing diffusion layers in many block ciphers and hash functions. However,
in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch
numbers offer a better balance between security and efficiency as a diffusion
layer, compared to MDS matrices. In this paper, we study NMDS matrices,
exploring their construction in both recursive and nonrecursive settings. We
provide several theoretical results and explore the hardware efficiency of the
construction of NMDS matrices. Additionally, we make comparisons between the
results of NMDS and MDS matrices whenever possible. For the recursive approach,
we study the DLS matrices and provide some theoretical results on their use.
Some of the results are used to restrict the search space of the DLS matrices.
We also show that over a field of characteristic 2, any sparse matrix of order
with fixed XOR value of 1 cannot be an NMDS when raised to a power of
. Following that, we use the generalized DLS (GDLS) matrices to
provide some lightweight recursive NMDS matrices of several orders that perform
better than the existing matrices in terms of hardware cost or the number of
iterations. For the nonrecursive construction of NMDS matrices, we study
various structures, such as circulant and left-circulant matrices, and their
generalizations: Toeplitz and Hankel matrices. In addition, we prove that
Toeplitz matrices of order cannot be simultaneously NMDS and involutory
over a field of characteristic 2. Finally, we use GDLS matrices to provide some
lightweight NMDS matrices that can be computed in one clock cycle. The proposed
nonrecursive NMDS matrices of orders 4, 5, 6, 7, and 8 can be implemented with
24, 50, 65, 96, and 108 XORs over , respectively
Decomposing Jacobians of Curves over Finite Fields in the Absence of Algebraic Structure
We consider the issue of when the L-polynomial of one curve over \F_q
divides the L-polynomial of another curve. We prove a theorem which shows that
divisibility follows from a hypothesis that two curves have the same number of
points over infinitely many extensions of a certain type, and one other
assumption. We also present an application to a family of curves arising from a
conjecture about exponential sums. We make our own conjecture about
L-polynomials, and prove that this is equivalent to the exponential sums
conjecture.Comment: 20 page
Complete Weight Enumerators of Generalized Doubly-Even Self-Dual Codes
For any q which is a power of 2 we describe a finite subgroup of the group of
invertible complex q by q matrices under which the complete weight enumerators
of generalized doubly-even self-dual codes over the field with q elements are
invariant.
An explicit description of the invariant ring and some applications to
extremality of such codes are obtained in the case q=4
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