Abstract In this paper, we investigate free Hermitian self-dual codes whose generator matrices are of the form [ I , A + v B ] over the ring F 2 + v F 2 = { 0 , 1 , v , 1 + v } with v 2 = v . We use the double-circulant, the bordered double-circulant and the symmetric construction methods to obtain free Hermitian self-dual codes of even length. By describing a new shortening method over this ring, we are able to obtain Hermitian self-dual codes of odd length. Using these methods, we also obtain a number of extremal codes. We tabulate the Hermitian self-dual codes with the highest minimum weights of lengths up to 50.

中文翻译：

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F2+vF2上的一种新的缩短方法和Hermitian自对偶码

摘要 在本文中，我们研究了自由 Hermitian 自对偶码，其生成矩阵在环 F 2 + v F 2 = { 0 , 1 , v , 1 + v } 上的形式为 [ I , A + v B ] ，其中v 2 = v 。我们使用双循环、有边双循环和对称构造方法来获得偶数长度的自由厄米自对偶码。通过在这个环上描述一种新的缩短方法，我们能够获得奇数长度的厄米自对偶码。使用这些方法，我们还获得了一些极值代码。我们将长度最长为 50 的最高最小权重的 Hermitian 自对偶码制表。