TY - JOUR
T1 - On the reconstruction of linear codes
AU - Maynard, Philip
AU - Siemons, Johannes
PY - 1998
Y1 - 1998
N2 - 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.
AB - 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.
U2 - 10.1002/(SICI)1520-6610(1998)6:4<285::AID-JCD6>3.0.CO;2-B
DO - 10.1002/(SICI)1520-6610(1998)6:4<285::AID-JCD6>3.0.CO;2-B
M3 - Article
VL - 6
SP - 285
EP - 291
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
SN - 1063-8539
IS - 4
ER -