Hamming code: Difference between revisions

Revision as of 01:07, 15 December 2022

Revision as of 01:27, 15 December 2022

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If the decoder does not attempt to correct errors, it can reliably detect triple bit errors. If the decoder does correct errors, some triple errors will be mistaken for single errors and "corrected" to the wrong value. Error correction is therefore a trade-off between certainty (the ability to reliably detect triple bit errors) and resiliency (the ability to keep functioning in the face of single bit errors).

This extended Hamming code iswas popular in computer memory systems, starting with [[IBM 7030 Stretch]] in 1961{{citation neededsfn|Kythe|Kythe|2017|datep=October 2019115}}, where it is known as ''SECDED'' (or SEC-DED, abbreviated from ''single error correction, double error detection'') {{citation neededsfn|Kythe|Kythe|2017|datep=October 201995}}. Server Particularlycomputers popularin is21st century, while typically keeping the (72SECDED level of protection,64) codeno longer use the Hamming's method, arelying truncatedinstead on the designs with longer codewords (127,120)128 Hammingto code256 plusbits anof additionaldata) parityand bitmodified balanced parity-check trees.{{citation neededsfn|dateKythe|Kythe|2017|p=October 2019115}} The (72,64) whichHamming hascode theis samestill spacepopular overheadin assome ahardware (9designs,8) parityincluding code[[Xilinx]] [[FPGA]] families.{{sfn|Kythe|Kythe|2017|p=115}}

==[7,4] Hamming code==