Which of the following explains why a code that has minimal distance k +1 must be k-error detecting. O f any time a codeword Cis sent and k errors occur those errors are detected, then it must be that...

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Extracted text: Which of the following explains why a code that has minimal distance k +1 must be k-error detecting. O f any time a codeword Cis sent and k errors occur those errors are detected, then it must be that the result of those errors, another word D, cannot be a codeword (otherwise the errors would go undetected). This word D will be at distancek from C, so there cannot be another codeword that is at distance k from C. Hence the minimal distance is at least k + 1. O the minimal distance is k + 1, and a codeword C is sent, and k errors occur, then C will be changed into another word whose distance from C is exactly k. This cannot be another codeword, since the minimal distance is k + 1, so the errors will be detected. O the minimal distance is k + 1, and a codeword C is sent, and at most k errors occur, then C will be changed into another word whose distance from C is at most k. This cannot be another codeword, since the minimal distance is k + 1, so the errors will be detected. O If any time a codeword Cis sent and at most k errors occur those errors are detected, then it must be that the result of those errors, another word D, cannot be a codeword (otherwise the errors would go undetected). This word D will be at most distance k from C, so there cannot be another codeword that is at distance k or less from C. Hence the minin I distance is at least k +1.