The main aim of this dissertation is to discuss the orphan structures of Reed-Muller codes. To do that a method of combining two codes, known as outer product have been first discussed. Since Reed-Muller codes are outer products of a number of copies of the full binary spaces of length 2, it is logical to apply the notion of outer product in these codes to examine their properties. Especially, the structures of the cosets of the Reed-Muller codes have been presented with help of outer product. With this, we examined these cosets which have no ancestors, that is which are orphans. Finally, the covering property of these codes have been presented and generalized.

A Dissertation Submitted in Partial Fulfillment of the requirement for the Degree of Master of Science in Mathematics