On $Z_{2^k}$-Dual Binary Codes Full article
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IEEE Transactions on Information Theory
ISSN: 0018-9448 , E-ISSN: 1557-9654 |
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| Output data | Year: 2007, Volume: 53, Number: 4, Pages: 1532-1537 Pages count : 6 DOI: 10.1109/tit.2007.892787 | ||
| Tags | Gray map, Hadamard codes, MacWilliams identity, perfect codes, $Z_{2^k}$-linearity | ||
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Abstract:
A new generalization of the Gray map is introduced. The new generalization $\Phi: Z_{2^k}^n \to Z_{2}^{2^{k-1}n}$ is connected with the known generalized Gray map $\varphi$ in the following way: if we take two dual linear $Z_{2^k}$-codes and construct binary codes from them using the generalizations $\varphi$ and $\Phi$ of the Gray map, then the weight enumerators of the binary codes obtained will satisfy the MacWilliams identity. The classes of $Z_{2^k}$-linear Hadamard codes and co-$Z_{2^k}$-linear extended 1-perfect codes are described, where co-$Z_{2^k}$-linearity means that the code can be obtained from a linear $Z_{2^k}$-code with the help of the new generalized Gray map.
Cite:
Krotov D.S.
On $Z_{2^k}$-Dual Binary Codes
IEEE Transactions on Information Theory. 2007. V.53. N4. P.1532-1537. DOI: 10.1109/tit.2007.892787 WOS Scopus РИНЦ OpenAlex
On $Z_{2^k}$-Dual Binary Codes
IEEE Transactions on Information Theory. 2007. V.53. N4. P.1532-1537. DOI: 10.1109/tit.2007.892787 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 2, 2006 |
| Published online: | Mar 26, 2007 |
Identifiers:
| Web of science: | WOS:000245306000020 |
| Scopus: | 2-s2.0-34147161642 |
| Elibrary: | 13544944 |
| OpenAlex: | W1987121126 |