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Linear codes over signed graphs
April 20, 2019 Β· Declared Dead Β· π Designs, Codes and Cryptography
"No code URL or promise found in abstract"
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Authors
Jose Martinez-Bernal, Miguel A. Valencia, Rafael H. Villarreal
arXiv ID
1904.09487
Category
cs.IT: Information Theory
Cross-listed
math.AC,
math.AG,
math.CO
Citations
10
Venue
Designs, Codes and Cryptography
Last Checked
4 months ago
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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