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Modular andp-adic cyclic codes

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Abstract

This paper presents some basic theorems giving the structure of cyclic codes of lengthn over the ring of integers modulop a and over thep-adic numbers, wherep is a prime not dividingn. An especially interesting example is the 2-adic cyclic code of length 7 with generator polynomialX 3 +λX 2 +(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.

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  1. Mathematical Sciences Research Center, AT&T Bell Laboratories, 07974, Murray Hill, NJ

    A. R. Calderbank & N. J. A. Sloane

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  1. A. R. Calderbank
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  2. N. J. A. Sloane
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Calderbank, A.R., Sloane, N.J.A. Modular andp-adic cyclic codes. Des Codes Crypt 6, 21–35 (1995). https://doi.org/10.1007/BF01390768

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