Heise, Werner and Quattrocchi, Pasquale:
Il teorema di equivalenza per i codici ciclici
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 78 (1985), fasc. n.6, p. 263-267, (Italian)
pdf (613 Kb), djvu (552 Kb). | MR 0919018 | Zbl 0624.94010
Sunto
Every unit $u$ in the ring $\mathbf{Z}_{n}$ of the residual classes mod $n$ induces canonically an automorphism $\pi$ of the algebra $\mathbf{R}_{n}(q) = GF (q) [z] / (z^{n}-1)$. Let $\mathcal{C} \subset \mathbf{R}_{n}(q)$ be a cyclic code, i.e. an ideal. If the numbers $n$ and $q$ are relatively prime then there exists a well-known characterization of the code $\pi (\mathcal{C})$. We extend this characterization to the general case.
Referenze Bibliografiche
[1]
I.F. BLAKE -
R.C. MULLIN (
1975) -
The Mathematical Theory of Coding,
Acad. Press New York et al.,
45. |
MR 396055 |
Zbl 0318.94009[2]
W. HEISE (
1982) -
The full equivalence theorem for cyclic codes,
Atti del Convegno di Geometria Combinatoria, Passo Mendola, 4-11 luglio 1982. |
Zbl 0546.94013[3]
W. HEISE e
P. QUATTROCCHI (
1983) -
Informations und Codierungsthéorie,
Springer, Heidelberg et al.,
286. |
fulltext (doi) |
MR 1333889[4]
J.H. VAN LINT (
1975) -
Coding Theory, «
Lecture Notes in Math.»,
201,
Springer, Berlin et al., 48. |
Zbl 0224.94002[5]
F.J. MACWILLIAMS e
N.J.A. SLOANE (
1977) -
The Theory of Error-Correcting Codes,
North-Holland, Amsterdam et al.,
234. |
Zbl 0657.94010[6]
P. FILIP e
W. HEISE (
1984) -
Monomial code-isomorphisms, to appear in the
proceedings of the congress Combinatorics '84, Sept. 24-29, Bari-Italy. |
MR 861298 |
Zbl 0592.94013
Con il contributo del Ministero per i Beni e le Attività Culturali