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Problemy Peredachi Informatsii, 2006, Volume 42, Issue 4, Pages 65–76
(Mi ppi61)
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This article is cited in 11 scientific papers (total in 11 papers)
Coding Theory
An Extension Theorem for Arcs and Linear Codes
I. N. Landjeva, A. P. Roussevab a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
b Sofia University St. Kliment Ohridski, Faculty of Mathematics and Computer Science
Abstract:
We prove the following generalization to the extension theorem of Hill and Lizak:
For every nonextendable linear $[n,k,d]_q$ code,
$q=p^s$,
$(d,q)=1$, we have
$$
\sum_{i\not\equiv0,d\,(\mathrm{mod}\;q)}A_i>q^{k-3}r(q),
$$
where $q+r(q)+1$ is the smallest size of a nontrivial blocking set in $\mathrm{PG}(2,q)$. This result is
applied further to rule out the existence of some linear codes over $\mathbb F_4$ meeting the Griesmer
bound.
Received: 15.11.2005 Revised: 27.05.2006
Citation:
I. N. Landjev, A. P. Rousseva, “An Extension Theorem for Arcs and Linear Codes”, Probl. Peredachi Inf., 42:4 (2006), 65–76; Problems Inform. Transmission, 42:4 (2006), 319–329
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https://www.mathnet.ru/eng/ppi61 https://www.mathnet.ru/eng/ppi/v42/i4/p65
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Abstract page: | 263 | Full-text PDF : | 80 | References: | 41 | First page: | 2 |
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