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
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
Published In
Designs, Codes, and Cryptography
DOI
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
APA
Chicago
ICMJE
MLA
NLM
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.
Published In
Designs, Codes, and Cryptography
DOI
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