Models of encoding and decoding via Grobner basis for algebraic geometry codes and multidimensional cyclic codes

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Research results are classified into three subjects as follows. 1. Searching algebraic curves that have many rational points and searching efficient codes on algebraic curves and multidimensional cyclic codes. A method to compute Grobner basis for generalized quasi-cyclic codes has been established, and thereby, a searching method for them has been established. 2. Constructing unified models of encoding and decoding system for codes on algebraic curves. 3. Application of unified system of encoding and decoding for Reed-Solomon codes. The circuit scale of the unified system for the next-generation error-correcting codes has been estimated as 40% reduction of that of the conventional system.