Seminari IMAC sobre Estructures Algebraiques i Teoria de codis correctors d'errors: Optimal locally recoverable codes search.

10/11/2021 | imac
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El 16 de novembre  de 2021 a les 16:30  tindrà lloc la xerrada a càrrec de Helena Martín Cruz en el aula  TI2328DS.


Abstract:   Digital information is broadcasted through a certain channel after a previous encoding process and the use of a code. The form that the information adopts for this process is a sequence of symbols belonging to a finite set (typically a finite field). The code used will depend on the characteristics of the channel and our objectives or needs, such as, for example, correcting errors that may arise in the message transmitted as a result of the alterations that it suffers throughout its transmission through the channel. To solve this problem, the so-called error correction codes arise, which make it possible to recover the lost information from the rest of the information thanks to the properties of the code. These are usually block codes, that is, whose elements (codewords) are all of the same length, so they can be represented as vectors over the field used.
   
    As a particular case of error correcting codes we have the locally recoverable codes, which are characterized because any error in any coordinate of a codeword can be recovered from a set of other coordinates. There are Singleton-type bounds that relate the parameters of a locally recoverable code. The codes attaining equality are said to be optimal, and it is of this type on which we base our search.
   
    In this talk we will introduce the previous notions and specify the codes we work with, detailing the recovery method that we use that make them locally recoverable. Moreover, we will see some examples about the search for optimality for this specific type of codes.