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Linear codes over signed graphs (1904.09487v2)
Published 20 Apr 2019 in cs.IT, math.AC, math.AG, math.CO, and math.IT
Abstract: We give formulas, in terms of graph theoretical invariants, for the minimum distance and the generalized Hamming weights of the linear code generated by the rows of the incidence matrix of a signed graph over a finite field, and for those of its dual code. Then we determine the regularity of the ideals of circuits and cocircuits of a signed graph, and prove an algebraic formula in terms of the multiplicity for the frustration index of an unbalanced signed graph.
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