ns. A typical characteristic of linear block codes is a systematic structure in which the information bits form a contiguous string and the check bits are appended to the information bits as another contiguous string to form a codeword, termed a linear systematic block code. An important property of a linear block code is the minimum distance, dmin, between valid or error free codewords in the codespace. From this characteristic it is seen that the maximum number of detectable errors is equal to dmin - 1. The random error correcting capability, t, of a block code is equal to the largest integer which is not greater than (dmin - 1)/2. The Hamming codes are the first class of linear block codes which were devised for error correction; these codes and their variations have been widely used in digital communications and data storage systems. For any positive integer, m>3, there exists at least one Hamming code with the following properties: Code Length: n = 2m - 1 Information Bits: k = 2m 1 Capability: t = 1 | (dmin = 3 ) Check Bits: (n k) = m The characteristics of several Hamming codes are indicated in Table 6-1. Characteristics of Hamming Codes Information Check Length [ (n k) ] Table 6-1. Characteristics of Hamming Codes Shortened Hamming codes are created by deleting columns from the generator matrix and producing a set of codes with the following properties: Code Length: n = 2m - l - 1 Information Bits: k = 2m - - m - 1 - 1 Capability: t = 1 | (dmin = 4) Check Bits: (n - k) = m For a code to be useful for high speed memory applications, its structure must permit rapid parallel encoding and decoding Characteristics of Hsiao's Codes operations. Hsiao developed the SEC- Information Check Relative Typical DEC codes by examining the properties of Length Arithmetic Arithmetic shortened Hamming codes to identify [ (n k) ] Complexity specific codes which enable fast encoding and decoding processes. The properties of Hsiao's codes are described in Table 6- Depicted in this table are the characteristics of the code (n,k)