论文标题
$ gf（q）$的自偶代码带有对称发电机矩阵
Self-dual codes over $GF(q)$ with symmetric generator matrices
论文作者
论文摘要
我们引入了一种一致，有效的方法，以构建$ gf（q）$的自偶代码，并从$ q \ equiv 1 \ pmod 4 $的$ gf（q）$上构建对称发电机矩阵。使用这种方法，我们改善了最著名的自动偶数代码的最低权重，这些代码在近二十年中一直没有显着改善。我们专注于一类自动划分代码，包括双循环代码。使用我们的方法，称为“对称建筑”结构，我们获得了$ gf（13）$和$ gf（17）$的许多新的自偶代码（17）$，并提高了最低最低二重二重要代码的最低长度的最小值，最高40。这些是：A [20,10,10] QR自动二线代码超过$ GF（23）$，两个[24,12,12] QR QR自动二线代码超过$ GF（29）$（29）$和$ GF（41）$，以及a [32,12,12,14] QR自duals QR自dual代码超过$ GF（19）$。到目前为止，它们的最小重量最高。
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the best-known minimum weights of self-dual codes, which have not significantly improved for almost two decades. We focus on a class of self-dual codes, including double circulant codes. Using our method, called a `symmetric building-up' construction, we obtain many new self-dual codes over $GF(13)$ and $GF(17)$ and improve the bounds of best-known minimum weights of self-dual codes of lengths up to 40. Besides, we compute the minimum weights of quadratic residue codes that were not known before. These are: a [20,10,10] QR self-dual code over $GF(23)$, two [24,12,12] QR self-dual codes over $GF(29)$ and $GF(41)$, and a [32,12,14] QR self-dual codes over $GF(19)$. They have the highest minimum weights so far.
