Construction of a (64,237 ,12) Code via Galois Rings

Journal Article

Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock and Preparata codes, which exist for all lengths 4m ≥ 16. At length 16 they coincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 237, 12) code as the binary image, under the Gray map, of an extended cyclic code defined over the integers modulo 4 using Galois rings. The Nordstrom-Robinson code is defined in this same way, and like the Nordstrom-Robinson code, the new code is better than any linear code that is presently known.

Duke Authors

Cited Authors

  • Calderbank, AR; Mcguire, G

Published Date

  • 1997

Published In

  • Designs, Codes, and Cryptography

Volume / Issue

  • 10 / 2

Start / End Page

  • 157 - 165