Extension of Mathematical Software in Code Theory

Code theory is based on studying methods to determine the most economical, fast and secure way to transmit a message through a channel avoiding possible noise interference. To achieve a more reliable and accurate communication, messages are encoded using so-called error-correcting codes. The main goal of this project is to contribute to the process of developing a Magma software library that works with nonlinear codes in an efficient way. We will focus on the design and implementation of five functions related to systematic codes. These are: IsInformationSet(C, I), IsSystematic(C), InformationSpace(C), InformationSet(C), and AllInformationSets(C), where C is a non necessarily linear code and $I$ a set of coordinate positions. We will design different algorithms for each function, we will test theoretical results to improve the efficiency of some algorithms, we will create some tests to approve the functions and finally, we will do a performance study of all the proposed algorithms.