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

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Abstract

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 paritycheck matrices or by the constraint that the modulo-2 sum of all rows is equal to the all-zero vector in Hsiao paritycheck 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 paritycheck matrices with faster hardware implementations can be found. Moreover, special instantiations of these matrices enable the detection of all triple-bit and quadruplebit burst errors. (This is an updated version of the IOLTS'11 paper.)
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Dates and versions

cea-03635089 , version 1 (08-04-2022)

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Samuel Evain, Nathaniel Seymour, Yannick Bonhomme, Valentin Gherman. Generalized parity-check matrices for SEC-DED codes with fixed parity. IOLTS 2011 - 2011 IEEE 17th International On-Line Testing Symposium, Jul 2011, Athens, Greece. pp.198-201, ⟨10.1109/IOLTS.2011.5993842⟩. ⟨cea-03635089⟩

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