Modular and p-adic cyclic codes
<|reference_start|>Modular and p-adic cyclic codes: This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo p^a 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^3 + lambda X^2 + (lambda - 1) X - 1, where lambda satisfies lambda^2 - lambda + 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.<|reference_end|>
@article{calderbank2003modular,
    title={Modular and p-adic cyclic codes},
    author={A. R. Calderbank, N. J. A. Sloane},
    journal={Designs, Codes and Cryptography, Vol. 6 (1995), 21-35},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0311319},
    primaryClass={math.CO cs.IT math.IT}
}