Generalized parity-check matrices for SEC-DED codes with fixed parity

Hsiao and extended Hamming parity-check matrices can be used to define systematic linear block codes for Single Error Correction-Double Error Detection (SEC-DED). Their fixed code word parity enables the construction of low density parity-check matrices and fast hardware implementations. Fixed code word parity is enabled by an all-one row in extended Hamming parity-check matrices or by the constraint that the modulo-2 sum of all rows is equal to the all-zero vector in Hsiao parity-check matrices. In this paper, we show that these two constraints are particular instantiations of a more general constraint which involves an arbitrary number of rows in the parity-check matrix. As a consequence, sparser parity-check matrices with faster hardware implementations can be found. Moreover, special instantiations of these matrices enable the detection of all triple-bit and quadruple-bit burst errors.