For any prime p and n ⋛ 3, we examine p-ary linear codes generated by incidence matrices of two classes of graphs, Hn and Γn where Hn−1 is an induced subgraph of Γn. Γn is a subgraph of the union of the categorical product of triangular graphs Tn and complete graphs Kn, and complements of triangular graphs Tn and Kn, where the union of graphs is as defined in [4]. For the codes of Hn, we exhibit permutation decoding sets of order n for full error correction. Their size is only twice the lower bound due to Gordon [7]. We also consider partial permutation decoding for the binary codes from Γn.
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机译：对于任何素数p和n⋛3，我们检查由两类图的入射矩阵H n 和Γ n 生成的p元线性代码，其中H n-1 是Γ n 的诱导子图。 Γ n 是三角图T n 和完全图K n 的分类积的并集的子图，是三角图T的补码 n 和K n ，其中图的并集如[4]中所定义。对于H n 的代码，我们展示了n阶的置换解码集，用于完全纠错。由于戈登[7]，它们的大小仅为下限的两倍。我们还考虑对来自Γ n 的二进制代码进行部分置换解码。
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