A linear construction for certain kerdock and preparata codes
Publication
, Journal Article
Calderbank, AR; Hammons, AR; Kumar, PV; Sloane, NJA; Solé, P
Published in: Bulletin of the American Mathematical Society
January 1, 1993
The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre-parata codes are shown to be linear over ℤ4, the integers mod 4. The Kerdock and Preparata codes are duals over ℤ4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over ℤ4. This provides a simple definition for these codes and explains why their Hamming weight distributions are dual to each other. First-and second-order Reed-Muller codes are also linear codes over ℤ4, but Hamming codes in general are not, nor is the Golay code. © 1993 American Mathematical Society.
Duke Scholars
Published In
Bulletin of the American Mathematical Society
DOI
ISSN
0273-0979
Publication Date
January 1, 1993
Volume
29
Issue
2
Start / End Page
218 / 222
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Calderbank, A. R., Hammons, A. R., Kumar, P. V., Sloane, N. J. A., & Solé, P. (1993). A linear construction for certain kerdock and preparata codes. Bulletin of the American Mathematical Society, 29(2), 218–222. https://doi.org/10.1090/S0273-0979-1993-00426-9
Calderbank, A. R., A. R. Hammons, P. V. Kumar, N. J. A. Sloane, and P. Solé. “A linear construction for certain kerdock and preparata codes.” Bulletin of the American Mathematical Society 29, no. 2 (January 1, 1993): 218–22. https://doi.org/10.1090/S0273-0979-1993-00426-9.
Calderbank AR, Hammons AR, Kumar PV, Sloane NJA, Solé P. A linear construction for certain kerdock and preparata codes. Bulletin of the American Mathematical Society. 1993 Jan 1;29(2):218–22.
Calderbank, A. R., et al. “A linear construction for certain kerdock and preparata codes.” Bulletin of the American Mathematical Society, vol. 29, no. 2, Jan. 1993, pp. 218–22. Scopus, doi:10.1090/S0273-0979-1993-00426-9.
Calderbank AR, Hammons AR, Kumar PV, Sloane NJA, Solé P. A linear construction for certain kerdock and preparata codes. Bulletin of the American Mathematical Society. 1993 Jan 1;29(2):218–222.
Published In
Bulletin of the American Mathematical Society
DOI
ISSN
0273-0979
Publication Date
January 1, 1993
Volume
29
Issue
2
Start / End Page
218 / 222
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics