Z(8)-cyclic codes and quadratic residue codes

A set of n-tuples over Z(8) is called a code over Z(8) or a Z(8) code if it is a Z(8) module. A particularly interesting family of Z(8)-cyclic codes a re quadratic residue codes. We define such codes in terms of their idempote nt generators and show that these codes also have many good properties whic h are analogous in many respects to properties of quadratic residue codes o ver a field. In particular we show that the quadratic residuce codes over Z (8) have large automorphism groups which will be useful in decoding these c odes by using the powerful permutation decoding methods described by F. J. MacWilliams and N. J. A. Sloane (1978, "Theory of Error-Correcting Codes," North-Holland, Amsterdam). We also define a distance preserving map from Z( 8)(n) (Lee distance) to Z(2)(4n) (Hamming distance). (C) 2000 Academic Pres s.