Publications [#235822] of Robert Calderbank

Journal articles or Book chapters PUBLISHED

1. Calderbank, AR; Mcguire, G, Construction of a (64,237,12) Code via Galois Rings, Designs Codes and Cryptography, vol. 10 no. 2 (January, 1997), pp. 157-165 [doi]
   (last updated on 2026/01/17)

   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 4^m ≥ 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.