Modular and p-adic cyclic codes

Journal Article (Journal Article)

This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo p 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 X +λX +(λ-1)X-1, where λ satisfies λ - 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. a 3 2 2

Full Text

Duke Authors

Cited Authors

  • Calderbank, AR; Sloane, NJA

Published Date

  • July 1, 1995

Published In

Volume / Issue

  • 6 / 1

Start / End Page

  • 21 - 35

Electronic International Standard Serial Number (EISSN)

  • 1573-7586

International Standard Serial Number (ISSN)

  • 0925-1022

Digital Object Identifier (DOI)

  • 10.1007/BF01390768

Citation Source

  • Scopus