We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have computed the minimum distance for the codes corresponding to matrices upper-bounded by any fixed, even rank. A conjecture is proposed for the cases where the upper bound is odd. At the end of the article, tables for the weights of these codes, for spaces of symmetric matrices up to order $5$, are given. We also correct typographical errors in Proposition 1.1/3.1 of [3], and in the last table, and we have rewritten Corollary 4.9 of that paper, and the usage of that Corollary in the proof of Proposition 4.10.

翻译：本文考虑有限域（奇特征）上由行列式簇导出的线性码，该簇源于有界秩的对称矩阵。推导出码字的重量公式，并利用该公式计算出对应于任意固定偶数秩上界矩阵的最小距离。针对上界为奇数的情形，本文提出一个猜想。文末给出了对称矩阵空间（阶数不超过5）的码重分布表。此外，我们修正了文献[3]中命题1.1/3.1的排版错误及末表的错漏，并重写了该文的推论4.9及其在命题4.10证明中的引用。