Fernando Hernando

Construction and decoding of matrix-product codes from nested codes

We consider matrix-product codes

Decoding of matrix-product codes

{[C_1\cdots C_s] \cdot A}

The dimension of subcode-subfields of shortened generalized Reed-Solomon codes

, where

Subfield-subcodes of Generalized Toric codes

{C_1, \ldots , C_s}

On the distance of stabilizer quantum codes from J-affine variety codes

are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular by columns matrix. The decoding algorithm decodes up to half of the minimum distance.

The log-canonical threshold of a plane curve

In earlier papers there were given formulae for the Poincare series of multi-index filtrations on the ring of germs of functions of two variables defined by collections of valuations corresponding to (reducible) plane curve singularities and by collections of divisorial ones. It was shown that the Poincare series of a collection of divisorial valuations determines the topology of the collection of divisors. Here we give a formula for the Poincare series of a general collection of valuations on the ring of germs of functions of two variables centred at the origin and prove a generalization of the statement that the Poincare series determines the topology of the collection.