Calderbank, AR; Sloane, NJA, *Modular andp-adic cyclic codes*,
Designs, Codes and Cryptography, vol. 6 no. 1
(July, 1995),
pp. 21-35 [doi] .
**Abstract:**

*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.*