Data Communications and Computer Networks by Pearson

Error Detection and Correction 115

codewordislessthand

min

;otherwise,errorscannotbedetected.Thisisbecauseifthenumberoferrorsin

acodewordisequaltoorgreaterthand

min

,thecodewordmaycorrespondtoanothervalidcodeword;as

aresult,thereceivermaynotbeabletodetecterrors.Theerror-detectionanderror-correctioncapabilities

ofanycodingtechniquelargelydependontheminimumHammingdistanceasexplainedbelow.

Toenablethereceivertoonlydetectupto  nerrorsinthecodeword,d

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mustbegreaterthanor

equalton + 1 .Forexample,ford

min

=5,uptofourerrorscanbedetectedinacodeword, ...