一类新的MDS symbol-pair码

A New Class of MDS symbol-pair Codes

为了对抗符号对(symbol-pair)读取信道中的符号对错误,符号对码应运而生。与经典纠错码类似,极小对距离越大,符号对码的纠错能力越强,因此,构造具有较大极小符号对距离的符号对码至关重要。根据多项式重根的判别方法,通过分析有限域F p上线性方程组的解,得到了一类最大距离可分的符号对(MDS symbol-pair)码,其长度为4 p,极小符号对距离为10。结果表明,在同样码长的情况下,新构造的MDS符号对码具有较大的极小符号对距离。

symbol-pair codes are designed to protect against pair-errors in data reading channels.Similar to classical error correction code,maximum distance separable(MDS)symbol-pair codes have the best error-correcting capability,so the construction of MDS symbol-pair codes is crucial in symbol-pair coding theory.In this paper,according to a method for distinguishing multiple roots of polynomials,we derive a new class of MDS symbol-pair codes with length of 4pand minimum symbol-pair distance of ten by analyzing the solutions of certain equations over finite fields.The result shows that our new MDS symbol-pair codes have a large minimum symbol-pair distance in the MDS symbol-pair codes with equal length.