Abstract
M-spotty byte error control codes are very effective for correcting/detecting errors in semiconductor memory systems that employ recent high-density RAM chips with wide I/O data (e.g., 8, 16, or 32 bits). In this case, the width of the I/O data is one byte. A spotty byte error is defined as random t-bit errors within a byte of length b bits, where 1 ≤ t < b. Then, an error is called an m-spotty byte error if at least one spotty byte error is present in a byte. M-spotty byte error control codes are characterized by the m-spotty distance, which includes the Hamming distance as a special case for t = 1 or t = b. The Mac Williams identity provides the relationship between the weight distribution of a code and that of its dual code. The present paper presents the Mac Williams identity for the m-spotty weight enumerator of m-spotty byte error control codes. In addition, the present paper clarifies that the indicated identity includes the Mac Williams identity for the Hamming weight enumerator as a special case.
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