Modular and p-adic cyclic codes
Publication
, Journal Article
Calderbank, AR; Sloane, NJA
Published in: Designs, Codes and Cryptography
July 1, 1995
This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo pa and over the p-adic numbers, where p is a prime not dividing n. An especially interesting example is the 2-adic cyclic code of length 7 with generator polynomial X3+λX2+(λ-1)X-1, where λ satisfies λ2 - λ + 2 = 0. This is the 2-adic generalization of both the binary Hamming code and the quaternary octacode (the latter being equivalent to the Nordstrom-Robinson code). Other examples include the 2-adic Golay code of length 24 and the 3-adic Golay code of length 12. © 1995 Kluwer Academic Publishers.
Duke Scholars
Published In
Designs, Codes and Cryptography
DOI
EISSN
1573-7586
ISSN
0925-1022
Publication Date
July 1, 1995
Volume
6
Issue
1
Start / End Page
21 / 35
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., & Sloane, N. J. A. (1995). Modular and p-adic cyclic codes. Designs, Codes and Cryptography, 6(1), 21–35. https://doi.org/10.1007/BF01390768
Calderbank, A. R., and N. J. A. Sloane. “Modular and p-adic cyclic codes.” Designs, Codes and Cryptography 6, no. 1 (July 1, 1995): 21–35. https://doi.org/10.1007/BF01390768.
Calderbank AR, Sloane NJA. Modular and p-adic cyclic codes. Designs, Codes and Cryptography. 1995 Jul 1;6(1):21–35.
Calderbank, A. R., and N. J. A. Sloane. “Modular and p-adic cyclic codes.” Designs, Codes and Cryptography, vol. 6, no. 1, July 1995, pp. 21–35. Scopus, doi:10.1007/BF01390768.
Calderbank AR, Sloane NJA. Modular and p-adic cyclic codes. Designs, Codes and Cryptography. 1995 Jul 1;6(1):21–35.
Published In
Designs, Codes and Cryptography
DOI
EISSN
1573-7586
ISSN
0925-1022
Publication Date
July 1, 1995
Volume
6
Issue
1
Start / End Page
21 / 35
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