论文标题
关于线性循环和constacyclic代码的等效性
On the equivalence of linear cyclic and constacyclic codes
论文作者
论文摘要
我们为线性循环代码在各个有限磁场上的置换和单一等效性提供了新的条件。我们记得，单一等效性和等距等效性与有限场上的线性代码相同。还给出了通过其定义集上的换档图的线性循环代码单一等效性的必要条件。此外，我们为$ \ mathbb {f} _4 $的constacyclic代码的单一等价提供了新的代数标准。最后，我们证明，如果$ \ gcd（3n，ϕ（3n））= 1 $，则所有置换等效的constacyclic constacyclic constacyclic constacyclic of $ n $ over $ \ mathbb {f} _4 $由乘数的动作给出。这项工作的结果使我们能够修剪新线性代码的搜索算法，并发现破纪录的线性和量子代码。
We introduce new sufficient conditions for permutation and monomial equivalence of linear cyclic codes over various finite fields. We recall that monomial equivalence and isometric equivalence are the same relation for linear codes over finite fields. A necessary and sufficient condition for the monomial equivalence of linear cyclic codes through a shift map on their defining set is also given. Moreover, we provide new algebraic criteria for the monomial equivalence of constacyclic codes over $\mathbb{F}_4$. Finally, we prove that if $\gcd(3n,ϕ(3n))=1$, then all permutation equivalent constacyclic codes of length $n$ over $\mathbb{F}_4$ are given by the action of multipliers. The results of this work allow us to prune the search algorithm for new linear codes and discover record-breaking linear and quantum codes.
