In this paper we consider some properties of quasi-cyclic codes over the integer residue rings. A quasi-cyclic code over Zk, the ring of integers modulo k, reduces to a direct product of quasi-cyclic codes over Zpi ei, k = &Pi:i = 1s piei, pi, a prime. Let T be the standard shift operator. A linear code C over a ring R is called an l-quasi-cyclic code if Tl(c) ∈ C, whenever c ∈ C. It is shown that if (m, q) = 1, q = pr, p a prime, then an l-quasi-cyclic code of length lm over Zq is a direct product of quasi-cylcic codes over some Galois extension rings of Zq. We have discussed about the structure of the generator of a 1-generator l- quasi-cyclic code of length lm over Zq. A method to obtain quasi-cyclic codes over Zq, which are free modules over Zq, has been discussed.
['Maheshanand Maheshanand', 'Siri Krishan Wasan']
On quasi-cyclic codes over integer residue rings