In this collection of works, the author and his collaborators give original answer to theoretical and practical current questions that correspond to open problems of different Mathematical branches: on one hand, Algebraic Geometry and Theory of Codes; and on the other hand, Approximation Theory and computer-assisted Geometric Design.

With these results, the authors have achieved a successful combination of theoretical results of high abstraction degree with the most rigorous and reliable computarized implementation, making possible the practical use of the so-called Algebraic Curved of small degree, to solve problems in different application domains that embrace from engineering design to the instrumentation of error corrective codes and Cripto - public keys’ systems. This last application is very interesting to codify the information to be transmitted by any means, for example, Internet.

Therefore, the results obtained have arisen the interest and deserved references from internationally prestigious scientists, and have been published in important magazines and proceedings of significant international events, such as Mathematicsche Nachrichten German magazine, published by Springer - Verlag, the proceedings of Coding Theory, Cryptography and Related Areas, also by Springer. One of its publishers is a noted editor of IEEE Transactions on Information Theory magazine. The results are gathered in a collection of 10 publications, one doctorate thesis and two master's degree theses from 1999 to 2001.