13,360 research outputs found
Incidence structures from the blown-up plane and LDPC codes
In this article, new regular incidence structures are presented. They arise
from sets of conics in the affine plane blown-up at its rational points. The
LDPC codes given by these incidence matrices are studied. These sparse
incidence matrices turn out to be redundant, which means that their number of
rows exceeds their rank. Such a feature is absent from random LDPC codes and is
in general interesting for the efficiency of iterative decoding. The
performance of some codes under iterative decoding is tested. Some of them turn
out to perform better than regular Gallager codes having similar rate and row
weight.Comment: 31 pages, 10 figure
The complexity of weighted boolean #CSP*
This paper gives a dichotomy theorem for the complexity of computing the partition
function of an instance of a weighted Boolean constraint satisfaction problem. The problem
is parameterized by a finite set F of nonnegative functions that may be used to assign weights to
the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems
correspond to the special case of 0,1-valued functions. We show that computing the partition
function, i.e., the sum of the weights of all configurations, is FP#P-complete unless either (1) every
function in F is of “product type,” or (2) every function in F is “pure affine.” In the remaining cases,
computing the partition function is in P
Applications of finite geometry in coding theory and cryptography
We present in this article the basic properties of projective geometry, coding theory, and cryptography, and show how
finite geometry can contribute to coding theory and cryptography. In this way, we show links between three research areas, and in particular, show that finite geometry is not only interesting from a pure mathematical point of view, but also of interest for applications. We concentrate on introducing the basic concepts of these three research areas and give standard references for all these three research areas. We also mention particular results involving ideas from finite geometry, and particular results in cryptography involving ideas from coding theory
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