In this paper, we introduce codes equipped with pomset block metric. A Singleton type bound for pomset block codes is obtained. Code achieving the Singleton bound, called a maximum distance separable code (for short, MDS (
$${\mathbb {P}},\pi $$
)-code) is also investigated. We extend the concept of I-perfect codes and r-perfect codes to pomset block metric. The relation between I-perfect codes and MDS
$$({\mathbb {P}},\pi )$$
-codes is also considered. When all blocks have the same dimension, we prove the duality theorem for codes and study the weight distribution of MDS ...
