Show simple item record Ghinelli, D. Key, J. D. McDonough, Thomas 2012-04-23T14:55:36Z 2012-04-23T14:55:36Z 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.other DSpace_20121128.csv: row: 4632
dc.identifier.other Scopus: 84891903077
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.contributor.institution Algebraic Combinatorics en
dc.contributor.institution Department of Physics en
dc.description.status Peer reviewed en

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