Algebraic-geometric codes over Z/sub 4/

A new class of Z/sub 4/-linear codes is constructed using algebraic-geometric tools and studied. Several known Z/sub 4/-linear codes arise as special cases with an underlying rational function field. Sharp bounds for the dimension and minimum Lee weights of these codes, including what may be interpreted as the BCH and Goppa bounds for Z/sub 4/-linear codes, are derived and some efficient codes are presented.