On MacWilliams type identities for -fold joint -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 joint m -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.