论文标题
几个不可还原的constacyclic和循环代码的家族
Several Families of Irreducible Constacyclic and Cyclic Codes
论文作者
论文摘要
在本文中，研究了有限领域及其双重的几个不可还原的constacyclic代码。这些不可还原的constacyclic代码的重量分布及其双重参数已解决。构建了几个具有几个权重的不可还原的康斯坦环境代码的家庭和几个最佳constacyclic代码家族。作为副产品，一个$ [2n，（n-1）/2，d \ geq 2（\ sqrt {n} +1）] $不可记录的$ \ gf（q）$的不可循环代码和$ [（q-1）n，（q-1）n，（n-1）/2，d \ geq（q-1）（n c cy sqrt+irred cyrt {cy sqrt {cy sqrt {出现了$ \ gf（q）$，其中$ n $是prime，因此$ \ ord_n（q）=（n-1）/2 $。本文中的结果补充了早期的作品，对有限领域的不可还原的constacyclic和循环代码作用。
In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several families of irreducible constacyclic codes with a few weights and several families of optimal constacyclic codes are constructed. As by-products, a family of $[2n, (n-1)/2, d \geq 2(\sqrt{n}+1)]$ irreducible cyclic codes over $\gf(q)$ and a family of $[(q-1)n, (n-1)/2, d \geq (q-1)(\sqrt{n}+1)]$ irreducible cyclic codes over $\gf(q)$ are presented, where $n$ is a prime such that $\ord_n(q)=(n-1)/2$. The results in this paper complement earlier works on irreducible constacyclic and cyclic codes over finite fields.
