Math @ Duke

Publications [#235822] of Robert Calderbank
Papers Published
 Calderbank, AR; Mcguire, G, Construction of a (64,2^{37},12) Code via Galois Rings,
Designs, Codes, and Cryptography, vol. 10 no. 2
(1997),
pp. 157165
(last updated on 2018/02/24)
Abstract: 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 NordstromRobinson 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 NordstromRobinson code is defined in this same way, and like the NordstromRobinson code, the new code is better than any linear code that is presently known.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

