COMBINATORICS A Webster-type definition of combinatorics is the study of the arrangement of, operations on, and selection of discrete mathematical elements belonging to finite sets or making up geometric configurations. Combinatorical methods have been used to solve problems in telecommunications and networking, cryptography, and in the design of computers. When transmitting data, errors can occur due to noise. To deal with this, error-correcting codes are used in many areas including for satellite transmissions and to store data on compact discs. These codes do not exist for all possible sets of parameters, so we may have to perform a search to determine if that code exists, and if so, determine its structure. This process is called a combinatorial search. The objective of HOUGHTEN and OMBUKI research is to develop efficient algorithms and programs to use in those searches.