  Sum-rank-metric codes have wide applications in the multishot network coding
and the distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes
and their Welch-Berlekamp type decoding algorithms were proposed and studied.
They are sum-rank versions of Reed-Solomon codes and BCH codes in the Hamming
metric. In this paper, we construct binary linear sum-rank-metric codes of the
matrix size $2 \times 2$, from BCH, Goppa and additive quaternary Hamming
metric codes. Larger sum-rank-metric codes than these sum-rank BCH codes of the
same minimum sum-rank distances are obtained. Then a reduction of the decoding
in the sum-rank-metric to the decoding in the Hamming metric is given. Fast
decoding algorithms of BCH and Goppa type binary linear sum-rank-metric codes
of the block length $t$ and the matrix size $2 \times 2$, which are better than
these sum-rank BCH codes, are presented. These fast decoding algorithms for BCH
and Goppa type binary linear sum-rank-metric codes of the matrix size $2 \times
2$ need at most $O(t^2)$ operations in the field ${\bf F}_4$. Asymptotically
good sequences of quadratic-time encodable and decodable binary linear
sum-rank-metric codes of the matrix size $2 \times 2$ satisfying
$$R_{sr}(\delta_{sr}) \geq
1-\frac{1}{2}(H_4(\frac{4}{3}\delta_{sr})+H_4(2\delta_{sr})),$$ can be
constructed from Goppa codes.
