Bazzi and Mitter [3] showed that binary dihedral group codes are asymptotically good. In this paper we prove that the dihedral group codes over any finite field with good mathematical properties are asymptotically good. If the characteristic of the field is even, we construct asymptotically good self-dual dihedral group codes. If the characteristic of the filed is odd, we construct both the asymptotically good self-orthogonal dihedral group codes, and the asymptotically good LCD dihedral group codes.
翻译:Bazzi 和 Mitter [3] 显示二进制二进制二进制组的代码在性质上是无损的。 在本文中, 我们证明任何具有良好数学属性的有限字段的二进制组的代码在性质上是无损的。 如果字段的特性是均衡的, 我们构建了无损的自相对立制组的代码。 如果存档的特性是奇异的, 我们既构建了无损自口式二进制组的代码, 也构建了无损式好的LCD二进制组的代码 。