COMPSCI 70 Chapter Notes - Chapter 9: Polynomial Interpolation, Lagrange Polynomial, Finite Field

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Error correcting codes embed messages into codewords, transmit the codeword, and recover the message from the damaged/corrupted symbols that are received. The codeword is redundant (i. e. it contains more packets than the original message to account for lost or corrupted packets) The contents of each packet is a number , or in , where is prime. There is a unique polynomial of degree such that for contains all of the information about the message, and evaluating gives the intended contents of the i-th packet. The message to be sent is now . We can generate additional packets by evaluating at additional points . Because we are working in modulo q, we must make sure that . Send packets to allow the original -length message to be recovered (where there are at most erasures and at most corruptions) Each packet has the size of size of the whole message (where is the size of the message)

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