符号图上的线性码
Linear codes over signed graphs
摘要：
本文利用图论不变量，给出了有限域上符号图的关联矩阵行生成的线性码的最小距离和广义Hamming重量的计算公式，以及它的对偶码的最小距离和广义Hamming重量的计算公式。在此基础上，我们确定了符号图的圈和余圈的理想的正则性，并证明了一个关于不平衡符号图挫折指数的重数代数公式。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
