Geometric spaces and efficient codes (Q1904267)

The theory of geometric spaces is used to construct new efficient error control codes. The emphasis is on single error correcting-double error detecting codes. Both encoding and decoding algorithms are given and analysed. A comparison is given with a shortened Hamming code to show that the new codes provide faster and less complex circuits for the whole coding process. The paper begins with a careful introduction of the basic ideas and proceeds gently to more complex considerations using several of the basic ideas of coding theory.