On a [formula omitted]-fold joint [formula omitted]-spotty Lee weight enumerator

Abstract

Nowadays, high speed memory systems having large capacity use high-density RAM chips with wide I/O data. These chips are prone to multiple random bit errors (known asm-spotty byte errors) when encountered with high energy particles. To detect or correct such errors, a new class of error-control codes called byte error-control codes have been introduced and studied. In this paper, we define and study a g-fold joint m-spotty Lee 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 derive some MacWilliams type identities for this enumerator.