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

Publication ,  Journal Article
Calderbank, AR; Mcguire, G
Published in: Designs, Codes, and Cryptography
January 1, 1997
Published version (DOI)

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 Scholars

Robert Calderbank
Author Robert Calderbank Computer Science

Published In

Designs, Codes, and Cryptography

DOI

10.1023/A:1008240319733

ISSN

0925-1022

Publication Date

January 1, 1997

Volume

10

Issue

2

Start / End Page

157 / 165

Related Subject Headings

  • Computation Theory & Mathematics
  • 49 Mathematical sciences
  • 46 Information and computing sciences
  • 40 Engineering
  • 0804 Data Format
  • 0802 Computation Theory and Mathematics
  • 0101 Pure Mathematics
 

Citation

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Calderbank, A. R., & Mcguire, G. (1997). Construction of a (64,237,12) Code via Galois Rings. Designs, Codes, and Cryptography, 10(2), 157–165. https://doi.org/10.1023/A:1008240319733
Calderbank, A. R., and G. Mcguire. “Construction of a (64,237,12) Code via Galois Rings.” Designs, Codes, and Cryptography 10, no. 2 (January 1, 1997): 157–65. https://doi.org/10.1023/A:1008240319733.
Calderbank AR, Mcguire G. Construction of a (64,237,12) Code via Galois Rings. Designs, Codes, and Cryptography. 1997 Jan 1;10(2):157–65.
Calderbank, A. R., and G. Mcguire. “Construction of a (64,237,12) Code via Galois Rings.” Designs, Codes, and Cryptography, vol. 10, no. 2, Jan. 1997, pp. 157–65. Scopus, doi:10.1023/A:1008240319733.
Calderbank AR, Mcguire G. Construction of a (64,237,12) Code via Galois Rings. Designs, Codes, and Cryptography. 1997 Jan 1;10(2):157–165.
Journal cover image

Published In

Designs, Codes, and Cryptography

DOI

10.1023/A:1008240319733

ISSN

0925-1022

Publication Date

January 1, 1997

Volume

10

Issue

2

Start / End Page

157 / 165

Related Subject Headings

  • Computation Theory & Mathematics
  • 49 Mathematical sciences
  • 46 Information and computing sciences
  • 40 Engineering
  • 0804 Data Format
  • 0802 Computation Theory and Mathematics
  • 0101 Pure Mathematics