Optimal Ternary Cubic Two‐Weight Codes
Optimal Ternary Cubic Two‐Weight Codes
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DOI：
10.1049/cje.2018.04.010
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发表时间：
2018-07
影响因子：
1.2
通讯作者：
M. Shi;Daitao Huang;P. Solé
中科院分区：
文献类型：
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作者：
M. Shi;Daitao Huang;P. Solé
我们研究了迹码，定义了集合L，它是某27阶环的m次扩张的乘法群的一个子群。这些码是阿贝尔的，并且它们的三值映象是余索引3(又称.立方代码)。利用高斯和计算了它们的Lee权分布。当m为单偶数时，这些码有三个非零权重。当m为奇数时，在关于L码大小的一些假设下，我们得到了两个新的无穷族二重码，它们是最优的。文中还给出了图像码在秘密共享方案中的应用。
We study trace codes with defining set L, a subgroup of the multiplicative group of an extension of degree m of a certain ring of order 27. These codes are abelian, and their ternary images are quasi-cyclic of coindex three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly-even. When m is odd, under some hypothesises on the size of L, we obtain two new infinite families of two-weight codes which are optimal. Applications of the image codes to secret sharing schemes are also given.