Nowadays, error control codes have become an essential technique to improve the reliability of various digital systems. A new type error control codes called m-spotty byte error control codes are applied to computer memory systems. These codes are essential to make the memory systems reliable. Here, we introduce the m-spotty Rosenbloom-Tsfasman weights and m-spotty Rosenbloom-Tsfasman weight enumerator of linear codes over Fq[u]/(uk) with uk=0. We also derive a MacWilliams type identity for m-spotty Rosenbloom-Tsfasman weight enumerator.

Nonprimitive non-narrow-sense BCH codes have been studied by many scholars. In this paper, we utilize nonprimitive non-narrow-sense BCH codes to construct a family of asymmetric quantum codes and two families of quantum convolutional codes. Most quantum codes constructed in this paper are different from the ones in the literature. Moreover, some quantum codes constructed in this paper have good parameters compared with the ones in the literature.