On the reconstruction of linear codes

Philip Maynard, Johannes Siemons

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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.
Original languageEnglish
Pages (from-to)285-291
Number of pages7
JournalJournal of Combinatorial Designs
Issue number4
Publication statusPublished - 1998

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