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Similarly, knowledge of any t + 1 elements from the codeword suffices to determine the remaining elements of the codeword. The decoding function DEC can be applied as long as t + 1 elements from a codeword are available. A RS code is capable of error correction and detection. The task of error correction is to find the error locations and error values in a received vector. On the other hand, error detection means an indication that errors have occurred, without attempting to correct them. We recall the following well known result from coding theory.

Ravindran Algorithm 4. level ← L; 45 msg currentHead ← {root}; descend(parent, level)∩Qw (v); for level = L − 1, L − 2, . . level ← level; levelW rHead; 53 else δ ← d(v, levelHead); 54 noW riteQ ← true; currentHead ← levelHead; 55 break; procedure WriteQuorum (v, msg) 56 if noW riteQ = true then msg Qw (v); 57 break; if v ∈ Qr (v) is down then 58 if levelRdHead = ∅ and f ind(v) ← f alse; type = read then validAns(v) ← null; 59 f ind(v) ← true; validLevel(v) ← null; 60 break; for level = 1, . .

A BA protocol allows a set of parties, each holding some input bit, to agree on a common bit, even though some of the parties may act maliciously in order to make the honest parties disagree. The BC and BA primitives have been used as building blocks in several important secure distributed computing tasks such as Secure Multiparty Computation (MPC) [BOGW88, BKR94, RBO89], Verifiable Secret Sharing (VSS) [CGMA85, BOGW88, RBO89] etc. An important, practically motivated variant of BC and BA problem are asynchronous broadcast (known as A-cast) and asynchronous BA (known as ABA) that study the conventional BC and BA problems in asynchronous network settings.

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