On MacWilliams type identities for r-fold joint m-spotty weight enumerators

Nowadays, high-density RAM chips with wide I/O data (e.g., 16, 32 and 64 bits) are used in computer memory systems. When exposed to high-energy particles, these chips become highly susceptible to m-spotty byte errors, which can be effectively detected or corrected using (m-spotty) byte error-control codes. In this paper, we introduce the r-fold jointm-spotty weight enumerator of byte error-control codes over the ring of integers modulo ℓ(ℓ≥2 an integer) and over arbitrary finite fields. We also study some of its properties and establish some MacWilliams type identities for the same.