  Recently, $b$-symbol codes are proposed to protect against $b$-symbol errors
in $b$-symbol read channels. It is an interesting subject of study to consider
the complete $b$-symbol weight distribution of cyclic codes since $b$-symbol
metric is a generalization for Hamming metric. The complete $b$-symbol Hamming
weight distribution of irreducible codes is known in only a few cases. In this
paper, we give a complete $b$-symbol Hamming weight distribution of a class of
irreducible codes with two nonzero $b$-symbol Hamming weights.
