MacWilliams type identities for some new $m$-spotty weight enumerators

Abstract

Past few years have seen an extensive use of high-density RAM chips with wide I/O data (e.g., 16, 32, 64 bits) in computer memory systems. These chips are highly vulnerable to a special type of byte error, called an $m$-spotty byte error, which can be effectively detected or corrected using byte error-control codes. In this paper, we present joint $m$-spotty weight enumerator and split $m$-spotty weight enumerator for byte error-control codes over the ring of integers modulo $\ell$ ($\ell \geq 2$ is an integer) and over arbitrary finite fields. We also derive MacWilliams type identities for each of the aforementioned enumerators and discuss some of their applications.