论文标题
MDS和AMDS符号对代码是由重复的根代码构建的
MDS and AMDS symbol-pair codes are 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。在本文中，我们为具有代码长度$ lp $的两类MDS符号代码构建了更通用的发电机多项式。 Based on repeated-root cyclic codes, we derive all MDS symbol-pair codes of length $3p$, when the degree of the generator polynomials is no more than 10. We also give two new classes of (almost maximal distance separable) AMDS symbol-pair codes with the length $lp$ or $4p$ by virtue of repeated-root cyclic codes.对于长度$ 3p $，当发电机多项式的程度小于10时，我们会得出所有AMDS符号代码。 主要结果是通过确定有限场上某些方程的解。
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. In this paper, we construct more general generator polynomials for two classes of MDS symbol-pair codes with code length $lp$. Based on repeated-root cyclic codes, we derive all MDS symbol-pair codes of length $3p$, when the degree of the generator polynomials is no more than 10. We also give two new classes of (almost maximal distance separable) AMDS symbol-pair codes with the length $lp$ or $4p$ by virtue of repeated-root cyclic codes. For length $3p$, we derive all AMDS symbol-pair codes, when the degree of the generator polynomials is less than 10. The main results are obtained by determining the solutions of certain equations over finite fields.
