作者：Xiaodong; Han; Fei; Gaonetworkcodingerrorcorrectionhomomorphiclinearcode
摘要：In this work, the homomorphism ofthe classic linear block code in linear networkcoding for the case of binary field and its ex-tensions is studied. It is proved that the classiclinear error-control block code is homomor-phic network error-control code in networkcoding. That is, if the source packets at thesource node for a linear network coding areprecoded using a linear block code, then everypacket flowing in the network regarding tothe source satisfies the same constraints as thesource. As a consequence, error detection andcorrection can be performed at every interme-diate nodes of multicast flow, rather than onlyat the destination node in the conventionalway, which can help to identify and correct er-rors timely at the error-corrupted link and savethe cost of forwarding error-corrupted data tothe destination node when the intermediatenodes are ignorant of the errors. In addition,three examples are demonstrated which showthat homomorphic linear code can be com-bined with homomorphic signature, McEliecepublic-key cryptosystem and unequal errorprotection respectively and thus have a greatpotential of practical utility.
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