Cyclic codes of length 2e over Z4

Authors:
Taher Abualrub;Robert Oehmke
Affiliations:
American University of Sharjah, P.O. Box 26666 Sharjah, United Arab Emirates;University of Iowa, Iowa City, IA
Venue:
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Year:
2003

Citing 4
Cited 2

Modular and p-adic cyclic codes

Designs, Codes and Cryptography
The Mathematical Theory of Coding

The Mathematical Theory of Coding
Cyclic codes and quadratic residue codes over Z4

IEEE Transactions on Information Theory
Cyclic Codes over the Integers Modulopm

Finite Fields and Their Applications

Cyclic and negacyclic codes over the Galois ring GR(p2,m)

Discrete Applied Mathematics
Repeated Root Cyclic and Negacyclic Codes over Galois Rings

AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Quantified Score

Hi-index	0.00

Visualization

Abstract

Cyclic codes of odd length over Z4 have been studied by many authors. But what is the form of cylic codes of even length? The structure of cyclic codes of length n = 2e, for any positive integer e is considered. We show that any cyclic code is an ideal in the ring Rn=Z4[x]/〈xn - 1〉. We show that the ring Rn is a local ring but not a principal ideal ring. Also, we find the set of generators for cyclic codes. Examples of cyclic codes of such length are given.