(15 points) a) Build the Huffman coding tree and determine the codes for the following set of letters and weights: 3. 1 13 17 19 23 31 37 41 b) Encode DIGIT and assume a transmission error modified the seventh bit. Can you decode it anymore? Explain your answer. c) What is the expected cost length in bits of a message containing 5 characters for this frequency distribution before compression and after using Huffman coding