Exploring self-dual codes with Maple

This paper considers the use of Maple in exploring the properties of self-dual codes, a widely known class of linear error correcting codes. Insight into their structure can be achieved using invariant theory techniques, thus avoiding the need for lengthy and tedious algebraic computations, and encouraging their more detailed comprehension. A Maple session allows us to understand the reasoning behind the theory and find out how this structure really works. Several procedures are proposed for attacking this problem. This material is available for graduate seminars, or high level under-graduate courses for students with mathematics or engineering degrees, and some background in linear algebra, coding theory and Groebner basis. This paper will show both the present state, as well as future trends, of research into these structures and possible improvements of the procedures using computer algebra systems and in particular Maple.