Modular and p-adic cyclic codes
Designs, Codes and Cryptography
Quaternary Codes
On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings
Designs, Codes and Cryptography
Cyclic codes and quadratic residue codes over Z4
IEEE Transactions on Information Theory
New ternary quasi-cyclic codes with better minimum distances
IEEE Transactions on Information Theory
On the algebraic structure of quasi-cyclic codes .I. Finite fields
IEEE Transactions on Information Theory
Quasi-cyclic codes over Z4 and some new binary codes
IEEE Transactions on Information Theory
New binary one-generator quasi-cyclic codes
IEEE Transactions on Information Theory
A class of 1-generator quasi-cyclic codes
IEEE Transactions on Information Theory
Quasicyclic low-density parity-check codes from circulant permutation matrices
IEEE Transactions on Information Theory
On the algebraic structure of quasi-cyclic codes III: generator theory
IEEE Transactions on Information Theory
Cyclic Codes over the Integers Modulopm
Finite Fields and Their Applications
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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.