Optimal Two-Weight Codes From Trace Codes Over $\mathbb {F}_2+u\mathbb {F}_2$
Optimal Two-Weight Codes From Trace Codes Over $\mathbb {F}_2+u\mathbb {F}_2$
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DOI：
10.1109/lcomm.2016.2614934
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发表时间：
2016-10
期刊：
影响因子：
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通讯作者：
M. Shi;Yan Liu;P. Solé
中科院分区：
文献类型：
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作者：
M. Shi;Yan Liu;P. Solé
我们在环F2 T UF2上构建了一个无限的双级重量代码家族。这些代码定义为跟踪代码。它们具有阿贝尔法规的代数结构。他们的Lee重量分布是通过使用字符总和计算的。通过灰色映射，我们获得了一个无限的阿贝尔二进制两重量代码。通过应用Griesmer绑定，它们被证明是最佳的。给出了秘密共享计划的申请。
We construct an infinite family of two-Lee-weight codes over the ring F2 t uF2. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. By Gray mapping, we obtain an infinite family of abelian binary two-weight codes. They are shown to be optimal by application of the Griesmer bound. An application to secret sharing schemes is given.