Error correcting codes and cryptography: generalized weights of convolutional codes and shrinking generators

Abstract

Error-correcting and cryptographic codes are areas of interface between the subjects of Mathematics, Electrical Engineering and Computer Science. Due to this interdisciplinary nature, with the support of FAPESP through the Thematic Project Security and Reliability of Information: Theory and Practice (Process Fapesp 2013 / 25977-7), we decided to set up a scientific initiation group with nine undergraduate students from the Mathematics courses Applied, Electrical Engineering and Computing from Unicamp, in order to allow, in its initial formation, a contact where the various approaches can be added, enriching the experience of this group of students where we believe future researchers and developers of the area will emerge. The work organization will involve collective activities as well as individual activities. Designed as a medium-term project, the group is made up of students at a relatively early stage of their degree, so that in case of satisfactory performance, it will be possible to renew the project for another one or two years, allowing students to arrive relatively mature to graduate training. From the point of view of orientation, the group will involve a group of experienced researchers, including Marcelo Firer (Imecc-Unicamp, proponent of this proposal, coordinator of the Thematic Project), Sueli Irene Rodrigues Costa (Imecc-Unicamp, Reginaldo Palazzo Jr. (Feec-Unicamp, principal researcher of the Thematic Project), Ricardo Dahab (IC-Unicamp, principal researcher of the Thematic Project) and Sara Diaz Cardell (Imecc-Unicamp, postdoctoral fellow). The project will be organized in two stages, one of introductory study common to all the participants and a second stage in which the students will delve into specific topics, possibly working in pairs. It is important to highlight that the same text is being presented for the implementation of nine scientific initiation fellowships. This unusual configuration aims to allow students, after an initial introductory study, to know some of the foundations of the contents and approaches that merge and intercalate in this thematic project, students have more options to engage in the subtopics with which they identify the most. This is an important aspect, which aims to strengthen the transdisciplinary character that guided the formation of this thematic project. (AU)