In this paper, a generalized class of Modified Prime Sequence Code (MPSC), which is one of the signature codes for synchronous optical CDMA, is introduced. The generalized codes are constructed over extension fields GF(p~m), while MPSCs had been considered to be constructed over prime fields GF(p) only. A simple method to construct the new codes is shown. The generalized codes have the special correlation properties as same as the original MPSCs, and the fact can be shown not empirically but deductively. We also show the generalized MPSC is a class of MDS codes. Relationship between generalized MPSCs and some kind of FH codes, such as the Einarsson codes and the one-coincidence codes, is also investigated.
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