Construction of a (64, 2 ^{ 37}, 12) Codevia Galois Rings
Designs, Codes and Cryptography
Computational Discrete Mathematics
Construction of Extremal Type II Codes over \mbox{\zZ}_4
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
New ring-linear codes from dualization in projective Hjelmslev geometries
Designs, Codes and Cryptography
Hi-index | 754.84 |
Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock (1972) and Preparata (1968) codes that can be very simply constructed as binary images, under the Gray map, of linear codes over Z4 that are defined by means of parity checks involving Galois rings. This paper describes how Fourier transforms on Galois rings and elementary symmetric functions can be used to derive lower bounds on the minimum distance of such codes. These methods and techniques from algebraic geometry are applied to find the exact minimum distance of a family of Z 4. Linear codes with length 2m (m, odd) and size 2(2m+1-5m-2). The Gray image of the code of length 32 is the best (64, 237) code that is presently known. This paper also determines the exact minimum Lee distance of the linear codes over Z4 that are obtained from the extended binary two- and three-error-correcting BCH codes by Hensel lifting. The Gray image of the Hensel lift of the three-error-correcting BCH code of length 32 is the best (64, 232) code that is presently known. This code also determines an extremal 32-dimensional even unimodular lattice