We propose several new lower bounds on the bandwidth costs of MDS convertible codes using a linear-algebraic framework. The derived bounds improve previous results in certain parameter regimes and match the bandwidth cost of the construction proposed by Maturana and Rashmi (2022 IEEE International Symposium on Information Theory) for $r^F\le r^I\le k^F$, implying that our bounds are tight in this case.

翻译：我们利用线性代数框架提出了多个关于MDS可转换码带宽成本的新下界。所推导的下界在特定参数范围内改进了先前的结果，并且与Maturana和Rashmi（2022年IEEE信息论国际研讨会）提出的构造的带宽成本在$r^F\\le r^I\\le k^F$条件下相匹配，表明我们的下界在此情况下是紧致的。