论文标题
MDS和AMDS符号对代码由重复根代码构建
MDS and AMDS symbol-pair codes constructed from repeated-root codes
论文作者
论文摘要
Cassuto和Blaum在2010年引入的符号对代码旨在防止符号对读取通道中的对错误。符号纠正中的中央主题之一是构造最大距离（MDS）符号对代码，该代码具有最大的配对校正性能。基于重复的根环循环代码，我们为更通用的发电机多项式构建了两个类别的MDS符号代码，还为具有长度$ lp $的新类别提供了几乎一类MDS（AMDS）符号代码。此外，当发电机多项式的程度不超过10时，我们还会得出所有具有长度$ 3p $的MD和AMDS符号代码。通过确定有限场上的某些方程的解决方案，获得了主要结果。
Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable (MDS) symbol-pair codes that possess the largest possible pair-error correcting performance. Based on repeated-root cyclic codes, we construct two classes of MDS symbol-pair codes for more general generator polynomials and also give a new class of almost MDS (AMDS) symbol-pair codes with the length $lp$. In addition, we derive all MDS and AMDS symbol-pair codes with length $3p$, when the degree of the generator polynomials is no more than 10. The main results are obtained by determining the solutions of certain equations over finite fields.
