Show simple item record

dc.contributor.author Ghinelli, D.
dc.contributor.author Key, J. D.
dc.contributor.author McDonough, Thomas
dc.date.accessioned 2012-04-23T14:55:36Z
dc.date.available 2012-04-23T14:55:36Z
dc.date.issued 2014-01
dc.identifier.citation Ghinelli , D , Key , J D & McDonough , T 2014 , ' Hulls of codes from incidence matrices of connected regular graphs ' Designs, Codes and Cryptography , vol 70 , no. 1 , pp. 35-54 . DOI: 10.1007/s10623-012-9635-0 en
dc.identifier.issn 1573-7586
dc.identifier.other PURE: 175967
dc.identifier.other PURE UUID: 73f3e3ae-ea70-460f-8df8-e6be6df390fc
dc.identifier.other dspace: 2160/7822
dc.identifier.uri http://hdl.handle.net/2160/7822
dc.description D.Ghinelli, J.D.Key, T.P.McDonough. Hulls of codes from incidence matrices of connected regular graphs. Designs Codes and Cryptography, 2014, vol 70, pg 35-54. en
dc.description.abstract The hulls of codes from the row span over FpFp , for any prime p, of incidence matrices of connected k-regular graphs are examined, and the dimension of the hull is given in terms of the dimension of the row span of A + kI over FpFp , where A is an adjacency matrix for the graph. Ifp = 2, for most classes of connected regular graphs with some further form of symmetry, it was shown by Dankelmann et al. (Des. Codes Cryptogr. 2012) that the hull is either {0} or has minimum weight at least 2k−2. Here we show that if the graph is strongly regular with parameter set (n, k, λ, μ), then, unless k is even and μ is odd, the binary hull is non-trivial, of minimum weight generally greater than 2k − 2, and we construct words of low weight in the hull; if k is even and μ is odd, we show that the binary hull is zero. Further, if a graph is the line graph of a k-regular graph, k ≥ 3, that has an ℓ-cycle for some ℓ ≥ 3, the binary hull is shown to be non-trivial with minimum weight at most 2ℓ(k−2). Properties of the p-ary hulls are also established. en
dc.language.iso eng
dc.relation.ispartof Designs, Codes and Cryptography en
dc.rights en
dc.subject Incidence matrix en
dc.subject Graph en
dc.subject Code en
dc.subject Hull en
dc.subject Permutation decoding en
dc.subject 05B05 en
dc.subject 05C38 en
dc.subject 94B05 en
dc.title Hulls of codes from incidence matrices of connected regular graphs en
dc.type /dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article en
dc.description.version authorsversion en
dc.identifier.doi http://dx.doi.org/10.1007/s10623-012-9635-0
dc.contributor.institution Algebraic Combinatorics en
dc.contributor.institution Institute of Mathematics & Physics (ADT) en
dc.description.status Peer reviewed en


Files in this item

Aside from theses and in the absence of a specific licence document on an item page, all works in Cadair are accessible under the CC BY-NC-ND Licence. AU theses and dissertations held on Cadair are made available for the purposes of private study and non-commercial research and brief extracts may be reproduced under fair dealing for the purpose of criticism or review. If you have any queries in relation to the re-use of material on Cadair, contact is@aber.ac.uk.

This item appears in the following Collection(s)

Show simple item record

Search Cadair


Advanced Search

Browse

Statistics