论文标题
MDS符号对代码的构造最小距离七八
Constructions of MDS symbol-pair codes with minimum distance seven or eight
论文作者
论文摘要
提出了符号对代码，以防止符号对读取通道中的配对。最小符号对距离在确定误差校正功能和具有最大最小符号对距离的符号对代码的构造方面起着至关重要的作用。最大距离可分离（\，MDS \，）符号代码是最佳的，从某种意义上说，此类代码可以在单胎绑定中获得。在本文中，对于长度$ 5p $，两种新类的MDS符号对代码具有最小符号对距离七或八的代码是通过利用$ \ Mathbb {f} _ {p} $上的重复根环循环代码来构建的，其中$ p $是prip的。此外，我们还会得出一类具有最小符号对距离的MDS符号代码，七个且长度为4p $。
Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance plays a vital role in determining the error-correcting capability and the constructions of symbol-pair codes with largest possible minimum symbol-pair distance is of great importance. Maximum distance separable (\,MDS\,) symbol-pair codes are optimal in the sense that such codes can acheive the Singleton bound. In this paper, for length $5p$, two new classes of MDS symbol-pair codes with minimum symbol-pair distance seven or eight are constructed by utilizing repeated-root cyclic codes over $\mathbb{F}_{p}$, where $p$ is a prime. In addition, we derive a class of MDS symbol-pair codes with minimum symbol-pair distance seven and length $4p$.
