Show simple item record Ghinelli, D. Key, J. D. McDonough, Thomas 2012-04-23T14:55:36Z 2012-04-23T14:55:36Z 2014-01-03
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. 1-2 . , 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.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 F_p, 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 F_p, where A is an adjacency matrix for the graph. If p = 2, for most classes of connected regular graphs with some further form of symmetry, it was shown in P. Dankelmann, J. D. Key, and B. G. Rodrigues, 'Codes from incidence matrices of graphs', Des. Codes Cryptogr. (To appear, 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,lambda,mu), then, unless k is even and mu 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 mu is odd, we show that the binary hull is zero. Further, if a graph is the line graph of a k-regular graph, k>2, that has an l-cycle for some l>2, 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.contributor.institution Algebraic Combinatorics en
dc.contributor.institution Institute of Mathematics & Physics (ADT) en
dc.description.status Peer reviewed en

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