✦ LIBER ✦

On the reconstruction of linear codes

✍ Scribed by Philip Maynard; Johannes Siemons

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 160 KB
Volume: 6
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1998)6:4<285::aid-jcd6>3.0.co;2-b

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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