论文标题
$ \ mathbb {z} _4 $的Plotkin-Optimal两重量代码的一般家庭
A general family of Plotkin-optimal two-weight codes over $\mathbb{Z}_4$
论文作者
论文摘要
我们在$ \ mathbb {z} _4，$以及其权重分布的情况下，获得了Plotkin-Timal-Timal Twimal Twimal Twime Twiper jupter Projective代码的所有可能参数。我们通过构建一个无限的两个重量代码家族来展示具有这些参数及其重量分布的代码的存在。 Shi等人构建的先前已知代码。 （\ emph {des codes cryptogr。} {\ bf 88}（3）：1-13，2020）可以作为我们结果的特殊情况得出。我们还证明，$ \ Mathbb {z} _4 $的任何Plotkin-最佳的两级级别的重量代码的灰色图像具有与Calderbank和Kantor意义上的SU1类型SU1类型的某些两型二元投影代码相同的参数和权重分布（\ emph {fluld。
We obtain all possible parameters of Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4,$ together with their weight distributions. We show the existence of codes with these parameters as well as their weight distributions by constructing an infinite family of two-weight codes. Previously known codes constructed by Shi et al. (\emph{Des Codes Cryptogr.} {\bf 88}(3):1-13, 2020) can be derived as a special case of our results. We also prove that the Gray image of any Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4$ has the same parameters and weight distribution as some two-weight binary projective codes of type SU1 in the sense of Calderbank and Kantor (\emph{Bull. Lond. Math. Soc.} {\bf 18}:97-122, 1986).
