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- W2162140163 abstract "The hulls of codes from the row span over $${mathbb{F}_p}$$ , 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 $${mathbb{F}_p}$$ , 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 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." @default.
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- W2162140163 date "2012-03-25" @default.
- W2162140163 modified "2023-09-25" @default.
- W2162140163 title "Hulls of codes from incidence matrices of connected regular graphs" @default.
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- W2162140163 doi "https://doi.org/10.1007/s10623-012-9635-0" @default.
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