Generalized Reed---Muller codes over $${\mathbb{Z}_q}$$
Designs, Codes and Cryptography
On quasi-cyclic codes over integer residue rings
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On the construction of skew quasi-cyclic codes
IEEE Transactions on Information Theory
Skew quasi-cyclic codes over Galois rings
Designs, Codes and Cryptography
Some families of Z4-cyclic codes
Finite Fields and Their Applications
New ring-linear codes from dualization in projective Hjelmslev geometries
Designs, Codes and Cryptography
| Hi-index | 754.90 |
Previously, (linear) codes over Z4 and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z 4-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z4 produces a new binary code, a (92, 224, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials