In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and defining sets. Second, we construct quaternary linear codes via simplicial complexes and determine the weight distributions of these codes. Third, the weight distributions of the binary subfield codes of these quaternary codes are also computed by employing the general characterization. Furthermore, we present two infinite families of optimal linear codes with respect to the Griesmer Bound, and a class of binary almost optimal codes with respect to the Sphere Packing Bound. We also need to emphasize that we obtain at least 9 new quaternary linear codes.
翻译：在本文中,我们主要研究四线性代码及其二元子场代码。首先,我们从发电机矩阵和定义组的角度,获得了四线性代码及其二元子场代码之间的一般明确关系。第二,我们通过简易复合体建立四线性代码,并确定这些代码的重量分布。第三,这些四线性代码的二元子场代码的重量分布也通过使用一般特征来计算。此外,我们提出了关于Griesmer Bound的两组最佳线性代码,和关于环球包装圈的几近最佳的二元代码。我们还需要强调,我们至少获得了九种新的四元线性代码。
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