Error correcting codes are used on a daily basis in many applications, e.g. IBAN, ISBN, online banking systems, network codes, etc. Certain geometries over finite fields, for example projective planes, provide a good source for constructing such codes. The smallest projective plane has 7 points and 7 lines (google "Fano plane" to find a nice picture of it), and one can construct an error correcting code from it which has 16 codewords and is 1-error correcting. The aim of the project is to describe the relation between projective planes (or other geometries) and error-correcting codes.
Requirements: Analytic thinking, review of literature, basic knowledge of linear algebra.