Matrix product codes are generalizations of some well-known constructions of codes, such as Reed-Muller codes, $[u+v,u-v]$-construction, etc. Recently, a bound for the symbol-pair distance of a matrix product code was given in \cite{LEL}, and new families of MDS symbol-pair codes were constructed by using this bound. In this paper, we generalize this bound to the $b$-symbol distance of a matrix product code and determine all minimum $b$-symbol distances of Reed-Muller codes. We also give a bound for the minimum $b$-symbol distance of codes obtained from the $[u+v,u-v]$-construction, and use this bound to construct some $[2n,2n-2]_q$-linear $b$-symbol almost MDS codes with arbitrary length. All the minimum $b$-symbol distances of $[n,n-1]_q$-linear codes and $[n,n-2]_q$-linear codes for $1\leq b\leq n$ are determined. Some examples are presented to illustrate these results.

翻译：矩阵乘积码是若干经典码构造的推广，如里德-穆勒码、$[u+v,u-v]$构造等。近期，文献\cite{LEL}给出了矩阵乘积码的符号对距离的一个界限，并利用该界限构造了新的MDS符号对码族。本文将此界限推广至矩阵乘积码的$b$-符号距离，并确定了所有里德-穆勒码的最小$b$-符号距离。我们还给出了通过$[u+v,u-v]$构造所得码的最小$b$-符号距离的一个界限，并利用该界限构造了若干任意长度的$[2n,2n-2]_q$-线性$b$-符号几乎MDS码。对于$1\leq b\leq n$的情形，确定了所有$[n,n-1]_q$-线性码和$[n,n-2]_q$-线性码的最小$b$-符号距离。文中通过实例阐明这些结果。