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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

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ICMJE
MLA
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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.
Journal cover image

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