New Extremal Type II Codes Over Z_4
Designs, Codes and Cryptography
Type II Self-Dual Codes over Finite Rings and Even Unimodular Lattices
Journal of Algebraic Combinatorics: An International Journal
Affine Invariant and Cyclic Codes over p-adic Numbers and Finite Rings
Designs, Codes and Cryptography
Cyclic codes of length 2e over Z4
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Cyclic codes over Z4 of oddly even length
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Some constacyclic codes over Z2k and binary quasi-cyclic codes
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
A Criterion for Designs in {\tf="P101461" Z}_4-codes on the Symmetrized Weight Enumerator
Designs, Codes and Cryptography
Cyclic Codes Over$$\mathbb{Z}_{4}$$ of Even Length
Designs, Codes and Cryptography
Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2
Designs, Codes and Cryptography
Construction of self-dual codes over finite rings Zpm
Journal of Combinatorial Theory Series A
Minimal Trellis Construction for Finite Support Convolutional Ring Codes
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
On the Quasi-cyclicity of the Gray Map Image of a Class of Codes over Galois Rings
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
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
Generalized Reed---Muller codes over $${\mathbb{Z}_q}$$
Designs, Codes and Cryptography
On the minimum distance of some families of Z2k-linear codes
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
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
Designs, Codes and Cryptography
Finite Fields and Their Applications
Some families of Z4-cyclic codes
Finite Fields and Their Applications
Finite Fields and Their Applications
Cyclic Codes over the Integers Modulopm
Finite Fields and Their Applications
Codes over p-adic Numbers and Finite Rings Invariant under the Full Affine Group
Finite Fields and Their Applications
Finite Fields and Their Applications
New ring-linear codes from dualization in projective Hjelmslev geometries
Designs, Codes and Cryptography
| Hi-index | 754.84 |
A set of n-tuples over Z4 is called a code over Z4 or a Z4 code if it is a Z4 module. We prove that any Z4-cyclic code C has generators of the form (fh, 2fg) where fgh=xn-1 over Z4 and |C|=4deg g 2deg h. We also show that C⊥ has generators of the form (g*h*, 2f*g*). We show that idempotent generators exist for certain cyclic codes. A particularly interesting family of Z4 -cyclic codes are quadratic residue codes. We define such codes in terms of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over a field. We show that the nonlinear binary images of the extended QR codes of lengths 32 and 48 have higher minimum weights than comparable known linear codes