Research objectives and content
This proposal relates to three fundamental problems of finite geometry and specifically to the main conjecture concerning Maximum Distance Separable (MDS) Codes.
In recent years, advances towards solving the three fundamental problems have been made by a wide variety of mathematicians using a wide variety of techniques. The main conjecture has been proven in specific cases but a general proof remains unknown.
However, new methods, including those developed by the applicant have led to optimism that the main conjecture can and will be proven in the near future.
Training content (objective, benefit and expected impact)
The proposed research is expected to benefit the applicant's knowledge of coding theory and the solution of mathematical problems. Members of the proposed research group should also benefit from the applicants previous ex- perience with solving geometrical problems and computing. The applicant has two years industrial experience of computer programming and wide knowledge of mathematical packages which will be invaluable to all members of the group. The applicant has already published joint papers with two members of the research group.
Links with industry / industrial relevance (22) Of the research group The proposed host research group (Discrete Wiskunde, Technische Universitiet Eindhoven) have close links with Philips (Eindhoven) in-relation to the theory of codes. These links include a weekly seminar workshop attended by members of the research group and employees of Philips. The applicant has already participated at these seminars and has led discussions on Maximum Distance Separable codes, the topic of this proposal.