Code division multiple access using Hermitean codes

Reed-Solomon (RS) codes present some desirable properties that make them useful in the generation of hopping sequences, for frequency hopping code division multiple access (FH CDMA). The algebraic geometric codes include the RS codes as a special case, therefore it is natural to propose the former as a candidate to FH CDMA. In this article, a description of such codes, along with the relationship between the RS codes and the proposed algebraic geometric codes is presented. Algebraic geometric codes constructed over Hermitean curves are used to generate the frequency hopping sequences. A comparison with sequences generated using RS codes reveals that longer sequences can be obtained for the same number of hits and number of sequences. Some of the properties of algebraic geometric codes, which make them suitable to use in CDMA systems, will be discussed.