Linear codes over signed graphs
Information Theory
2020-09-10 v2 Commutative Algebra
Algebraic Geometry
Combinatorics
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.
Cite
@article{arxiv.1904.09487,
title = {Linear codes over signed graphs},
author = {Jose Martinez-Bernal and Miguel A. Valencia and Rafael H. Villarreal},
journal= {arXiv preprint arXiv:1904.09487},
year = {2020}
}
Comments
Des. Codes Cryptogr., to appear