论文标题
当可变长度代码符合误差检测领域
When Variable-Length Codes Meet the Field of Error Detection
论文作者
论文摘要
给定有限字母$ a $和二进制关系$τ\ subseteq a^*\ times a^*$，如果$ x $ x $ - {\ it独立}，如果$τ（x）\ cap x = \ emberySet $。给定$ a^*$上的准键$ d $（以\ cite {w31}）的含义和$ k \ ge 1 $，我们将关系$τ_{d，k} $由$（x，x，y）\ int phist t，in y in in in in in in If，k} $ if，if，if，if，if，if，$ d（x，x，y） \ cite {jk97，n21}，可以在$τ_{d，k} $的条件上表示可变长度代码的错误检测校正功能。关于前缀度量，因子一，以及与自由单体的（反）自动形态相关的每个准单体，我们检查这些条件是否可以针对给定的常规代码确定。
Given a finite alphabet $A$ and a binary relation $τ\subseteq A^*\times A^*$, a set $X$ is $τ$-{\it independent} if $ τ(X)\cap X=\emptyset$. Given a quasi-metric $d$ over $A^*$ (in the meaning of \cite{W31}) and $k\ge 1$, we associate the relation $τ_{d,k}$ defined by $(x,y)\inτ_{d,k}$ if, and only if, $d(x,y)\le k$ \cite{CP02}.In the spirit of \cite{JK97,N21}, the error detection-correction capability of variable-length codes can be expressed in term of conditions over $τ_{d,k}$. With respect to the prefix metric, the factor one, and every quasi-metric associated to (anti-)automorphisms of the free monoid, we examine whether those conditions are decidable for a given regular code.
