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Matrix product codes are generalizations of some well-known constructions ofcodes, such as Reed-Muller codes, $[u+v,u-v]$-construction, etc. Recently, abound 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 usingthis bound. In this paper, we generalize this bound to the $b$-symbol distanceof a matrix product code and determine all minimum $b$-symbol distances ofReed-Muller codes. We also give a bound for the minimum $b$-symbol distance ofcodes obtained from the $[u+v,u-v]$-construction, and use this bound toconstruct some $[2n,2n-2]_q$-linear $b$-symbol almost MDS codes with arbitrarylength. 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 arepresented to illustrate these results.

New bounds for $b$-Symbol Distances of Matrix Product Codes