MacWilliams Type Identities for Some New $m$ -Spotty Weight Enumerators

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 l (l ≥ 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.