Error control codes have extensively been applied to semiconductor memories using high density RAM chips with wide I/O data, e.g., with 8-bit or 16-bit I/O data. Recently, spotty byte errors called s-spotty byte errors are newly defined as t or fewer bits errors in a byte having length b bits, where 1 ≤ t ≤ b. This paper proposes another type of spotty byte errors, i.e., m-spotty byte errors, where more than t bits errors in a byte may occur due to hit by high energetic particles. For these errors, this paper presents generalized m-spotty byte error control codes with minimum m-spotty distance d.

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. A spotty byte error is defined as t-bit errors within a byte of length b-bit, where 1 ≤ t ≤ b, and denoted as t/b-error. This paper proposes a new error model of two spotty byte errors occurring simultaneously, i.e., t/b-error and t′/b-error, where t t′, called complex spotty byte errors. This paper presents two complex m-spotty byte error control codes, i.e., St/bEC-(St/b+St′/b)ED codes which correct all single t/b-errors and detect both t/b-errors and t′/b-errors simultaneously, and (St/b+St′/b)EC codes which correct both single t/b-errors and single t′/b-errors simultaneously. This paper also presents practical examples of the codes with parameter t′=1, that is, St/bEC-(St/b+S)ED codes and (St/b+S) EC codes which require smaller check-bit length than the existing Single t/b-error Correcting and Double t/b-error Detecting (St/bEC-Dt/bED) codes and the Double t/b-error Correcting (Dt/bEC) codes, respectively.

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 MacWilliams identity provides the relationship between the weight distribution of a code and that of its dual code. The present paper presents the MacWilliams 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 MacWilliams identity for the Hamming weight enumerator as a special case.