1 Error-Detecting Codes Suppose Alice wants to transmit a message of n symbols, so that Bob is able to detect rather than correct any errors that have occured on the way. That is, Alice wants to find an encoding so that Bob, upon receiving the code, is able to either (I) tell that there are no errors and decode the message, or (II) realize that the transmitted code contains at least one error, and throw away the message Assuming that we are guaranteed a maximum of k errors, how should Alice extend her message (i.e. by how many symbols should she extend the message, and how should she choose these symbols)? You may assume that we work in GF(p) for very large prime p. Show that your scheme works, and that adding any lesser number of symbols is not good enough. 1 Error-Detecting Codes Suppose Alice wants to transmit a message of n symbols, so that Bob is able to detect rather than correct any errors that have occured on the way. That is, Alice wants to find an encoding so that Bob, upon receiving the code, is able to either (I) tell that there are no errors and decode the message, or (II) realize that the transmitted code contains at least one error, and throw away the message Assuming that we are guaranteed a maximum of k errors, how should Alice extend her message (i.e. by how many symbols should she extend the message, and how should she choose these symbols)? You may assume that we work in GF(p) for very large prime p. Show that your scheme works, and that adding any lesser number of symbols is not good enough