On the reconstruction of linear codes

Maynard, Philip and Siemons, Johannes (1998) On the reconstruction of linear codes. Journal of Combinatorial Designs, 6 (4). pp. 285-291. ISSN 1063-8539

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For a linear code over GF(q) we consider two kinds of “subcodes” called residuals and punctures. When does the collection of residuals or punctures determine the isomorphism class of the code? We call such a code residually or puncture reconstructible. We investigate these notions of reconstruction and show that, for instance, selfdual binary codes are puncture and residually reconstructible. A result akin to the edge reconstruction of graphs with sufficiently many edges shows that a code whose dimension is small in relation to its length is puncture reconstructible.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Algebra and Combinatorics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:26
Last Modified: 17 May 2023 00:38
URI: https://ueaeprints.uea.ac.uk/id/eprint/20873
DOI: 10.1002/(SICI)1520-6610(1998)6:4<285::AID-JCD6>3.0.CO;2-B

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