Modular and p-adic cyclic codes

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dc.creatorCalderbank, A. R.
dc.creatorSloane, N. J. A.
dc.date2003-11-18
dc.date.accessioned2026-07-07T08:18:15Z
dc.date.available2026-07-07T08:18:15Z
dc.descriptionThis 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.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0311319
dc.identifierhttp://arxiv.org/abs/math/0311319
dc.identifierDesigns, Codes and Cryptography, Vol. 6 (1995), 21-35
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134368
dc.subjectCombinatorics
dc.subjectInformation Theory
dc.subject94B15, 94B05
dc.titleModular and p-adic cyclic codes
dc.typetext

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