Math @ Duke

Publications [#236045] of Robert Calderbank
Papers Published
 Calderbank, AR; Sloane, NJA, Modular and padic cyclic codes,
Designs, Codes and Cryptography, vol. 6 no. 1
(1995),
pp. 2135, ISSN 09251022 [doi]
(last updated on 2018/06/20)
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 padic numbers, where p is a prime not dividing n. An especially interesting example is the 2adic cyclic code of length 7 with generator polynomial X3+λX2+(λ1)X1, where λ satisfies λ2  λ + 2 = 0. This is the 2adic generalization of both the binary Hamming code and the quaternary octacode (the latter being equivalent to the NordstromRobinson code). Other examples include the 2adic Golay code of length 24 and the 3adic Golay code of length 12. © 1995 Kluwer Academic Publishers.


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