Double Circulant Codes over Z\!Z_{\bf 4}and Even Unimodular Lattices
Journal of Algebraic Combinatorics: An International Journal
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
Isodual Codes over {\bb Z}_{2k} and Isodual Lattices
Journal of Algebraic Combinatorics: An International Journal
Self-dual Z4-codes and Hadamard matrices
Discrete Mathematics
Construction of Extremal Type II Codes over \mbox{\zZ}_4
Designs, Codes and Cryptography
Optimal Double Circulant Z4-Codes
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings
Designs, Codes and Cryptography
A Criterion for Designs in {\tf="P101461" Z}_4-codes on the Symmetrized Weight Enumerator
Designs, Codes and Cryptography
Higher Power Residue Codes and the Leech Lattice
Journal of Algebraic Combinatorics: An International Journal
Construction of self-dual codes over finite rings Zpm
Journal of Combinatorial Theory Series A
Construction of Z4-linear Reed-Muller codes
IEEE Transactions on Information Theory
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
Quaternary Plotkin constructions and quaternary Reed-Muller codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Galois rings and pseudo-random sequences
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Finite Fields and Their Applications
Cyclic Codes over the Integers Modulopm
Finite Fields and Their Applications
Finite Fields and Their Applications
Finite Fields and Their Applications
On the classification and enumeration of self-dual codes
Finite Fields and Their Applications
Finite Fields and Their Applications
New ring-linear codes from dualization in projective Hjelmslev geometries
Designs, Codes and Cryptography
On self-dual cyclic codes over finite chain rings
Designs, Codes and Cryptography
| Hi-index | 754.90 |
We construct new self-dual and isodual codes over the integers module 4. The binary images of these codes under the Gray map are nonlinear, but formally self-dual. The construction involves Hensel lifting of binary cyclic codes. Quaternary quadratic residue codes are obtained by Hensel lifting of the classical binary quadratic residue codes. Repeated Hensel lifting produces a universal code defined over the 2-adic integers. We investigate the connections between this universal code and the codes defined over Z4, the composition of the automorphism group, and the structure of idempotents over Z4. We also derive a square root bound on the minimum Lee weight, and explore the connections with the finite Fourier transform. Certain self-dual codes over Z4 are shown to determine even unimodular lattices, including the extended quadratic residue code of length q+1, where q≡-1(mod8) is a prime power. When q=23, the quaternary Golay code determines the Leech lattice in this way. This is perhaps the simplest construction for this remarkable lattice that is known