In this paper, we consider the convertible codes with the maximum distance separable (MDS) property, which can adjust the code rate according to the failure rates of devices. We first extend the notion of convertible codes to allow initial and final codes with different parameters. Then, we investigate the relationship between these parameters and thus establish new lower bounds on the access cost in the merge and split regimes. To gain a deeper understanding of access-optimal MDS convertible codes in the merge regime, we characterize them from the perspective of parity check matrices. Consequently, we present a necessary and sufficient condition for the access-optimal MDS convertible code in the merge regime. Finally, as an application of our characterization, we construct MDS convertible codes in the merge regime with optimal access cost based on the extended generalized Reed-Solomon codes.

翻译：本文研究具有最大距离可分(MDS)性质的可转换码，这类编码可根据设备故障率调整码率。我们首先扩展了可转换码的概念，允许初始码与最终码具有不同参数。随后探究这些参数之间的关系，从而在合并与分裂两种模式下建立了访问代价的新下界。为深入理解合并模式下访问最优的MDS可转换码，我们从校验矩阵的视角对其进行刻画，进而建立了合并模式下访问最优MDS可转换码的充要条件。最后，作为该刻画方法的应用，基于扩展的广义Reed-Solomon码构造了具有最优访问代价的合并模式MDS可转换码。