Paulo Almeida
Constructions for optimal convolutional codes
Convolutional codes are error correcting codes that are widely used to reliably transmit digital data over noisy communication channels, namely deep space communications. Optimal convolutional codes achieve the maximal distance possible, and can be obtained using superregular matrices. Emerging multimedia applications require error correction codes that have very different properties from classical codes. Optimal convolutional codes (1Dimensional and 2Dimensional) can be a good source of such codes, as was pointed out in the workshop Mathematical Coding Theory in Multimedia
Streaming in Banff International Research Station. In this talk, we present a general construction of superregular matrices over large finite fields, and explain how we used them to obtain 1D, 2D, and unit memory optimal convolutional codes.
Streaming in Banff International Research Station. In this talk, we present a general construction of superregular matrices over large finite fields, and explain how we used them to obtain 1D, 2D, and unit memory optimal convolutional codes.
Carla Reis
Completeness and Compactness of Quantale-enriched Categories
The powerful notion of quantale-enriched category allows a unifying description of several structures such as ordered sets and metric spaces in the setting of Category Theory. In this talk we will present some results relating topological and categorical properties with respect to Cauchy completeness and compactness. We will in particular explore the example of probabilistic metric spaces as categories enriched in the quantale of distribution functions.