Error correcting code for correcting single symbol errors and detecting double bit errors

摘要

Systems, apparatuses, and methods for generating error correction codes (ECCs) with two check symbols are disclosed. In one embodiment, a system receives a data word of length N−2 symbols, wherein N is a positive integer greater than 2, wherein each symbol has m bits, and wherein m is positive integer. The system generates a code word of length N symbols from the data word in accordance with a linear code defined by a parity check matrix. The parity check matrix is generated based on powers of γ, wherein γ is equal to β raised to the (2^m/4−1) power, β is equal to a raised to the (2^m/2+1) power, and α is a primitive element of GF(2^m). In another embodiment, the system receives a (N, N−2) code word and decodes the code word by generating a syndrome S from the code word using the parity check matrix.