On dual codes in the Doob schemes Full article
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IEEE International Symposium on Information Theory 07-12 Jul 2019 , Paris |
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| Journal |
IEEE International Symposium on Information Theory - Proceedings
ISSN: 2157-8095 |
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| Output data | Year: 2019, Volume: 2019, Pages: 1917-1921 Pages count : 5 DOI: 10.1109/isit.2019.8849850 | ||
| Tags | Association scheme, Doob graph, MacWilliams identity, | ||
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Abstract:
The Doob scheme D(m,n'+n'') is a metric association scheme defined on Em4×Fn'4×Zn''4, where E4=GR(4^2) or, alternatively, on Z2m4×Z2n'2×Zn''4. We prove the MacWilliams identities connecting the weight distributions of a linear or additive code and its dual. In particular, for each case, we determine the dual scheme, on the same set but with different metric, such that the weight distribution of an additive code C in the Doob scheme D(m,n'+n'') is related by the MacWilliams identities with the weight distribution of the dual code C* in the dual scheme. We note that in the case of a linear code C in Em4×Fn'4, the weight distributions of C and C* in the same scheme are also connected.
Cite:
Krotov D.S.
On dual codes in the Doob schemes
IEEE International Symposium on Information Theory - Proceedings. 2019. V.2019. P.1917-1921. DOI: 10.1109/isit.2019.8849850 WOS Scopus РИНЦ OpenAlex
On dual codes in the Doob schemes
IEEE International Symposium on Information Theory - Proceedings. 2019. V.2019. P.1917-1921. DOI: 10.1109/isit.2019.8849850 WOS Scopus РИНЦ OpenAlex
Dates:
| Published online: | Sep 26, 2019 |
Identifiers:
| Web of science: | WOS:000489100302003 |
| Scopus: | 2-s2.0-85073152808 |
| Elibrary: | 41689335 |
| OpenAlex: | W2976785461 |