Iván Blanco-Chacón

Nonuniform Fuchsian codes for noisy channels

We develop a new transmission scheme for additive white Gaussian noisy (AWGN) channels based on Fuchsian groups from rational quaternion algebras. The structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence conventional decoding methods based on linearity and symmetry do not apply. Previously, only brute force decoding methods with complexity that is linear in the code size exist for general nonuniform codes. However, the properly discontinuous character of the action of the Fuchsian groups on the complex upper half-plane translates into decoding complexity that is logarithmic in the code size via a recently introduced point reduction algorithm.

Differential operators and hyperelliptic curves over finite fields

Boix, De Stefani and Vanzo have characterized ordinary/supersingular elliptic curves over

Probability bounds for an eavesdropper's correct decision over a MIMO wiretap channel

\mathbb{F}_p

A higher order p-adic class number formula

in terms of the level of the defining cubic homogenous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve

Upper triangular operators and p-adic L-functions

\mathcal{C}

Fuchsian codes for AWGN channels

of genus

Quadratic modular symbols on Shimura curves

g\geq 2

Quadratic modular symbols

has level

Primes of the form n^2+n+p have density 1

2

International Workshop on Coding and Cryptography (WCC)April 2013, Bergen, Norway

. We provide a good number of examples and raise a conjecture.