Mac Williams Identity for m-Spotty Weight Enumerator

M-Spotty byte error control codes are very effective for correcting/detecting errors in semiconductor memory systems using recent high-density RAM chips with wide I/O data, e.g., 8, 16, or 32 bits. In this case, width of the I/O data is called a byte. A spotty byte error is defined as random i-bit errors within a byte of length 6-bit, where t les b. Especially, M-spotty byte error is defined as multiple spotty byte errors in a byte. M-spotty byte error control code is characterized by m-spotty distance which includes Hamming distance as a special case for t = 1 or t = b. The MacWilliams identity provides the relation of weight distribution of a code and that of its dual code. This paper presents the MacWilliams identity for m-spotty weight enumerator of the m-spotty byte error control codes. Also, this clarifies that the indicated identity includes the MacWilliams identity for Hamming weight enumerator as a special case.