Intersection problem for the class of Reed-Muller codes.

Abstract

The intersection problem for Coding Theory can be stated as follows: given a family or class of families of codes, find the spectrum of intersection numbers. The general strategy to attack this kind of problem begins by finding necessary conditions for the intersection. This leads to lower and upper bounds or a set of possible intersection numbers. Secondly, finding the sufficient conditions implies giving specific constructions of codes in such a way that the cardinality of their intersection fits those values between these bounds. In this dissertation is presented a complete solution of the intersection problem for the class of Reed-Muller codes.