There are many two-of-five codes that are commonly used. One example is the USPS POSTNET barcodes used in mail routing prior to 2013. These codes use a sequence of half height and full height bars to represent bits, with POSTNET in particular using full height bars for ones. Five such bits are used to represent one symbol, constrained that each 5 bit symbol has exactly two ones.

a) How many valid symbols are in this code?

b) What is the distance of this code?

c) If the probability of a bit error is p, what is the probability of an undetected symbol error?

d) If decimal digits are represented in standard BCD and a parity bit added, this will also generate a 5 bit code. How many valid symbols are in this code? What is the distance of this code?

e) What advantage would the two-of-five code offer over the BCD+parity code?

f) POSTNET further defined use of 12 symbols, including 9 zip+4 digits, a 2 digit location code, and a checkdigit calculated such that the sum of all of the digits is a multiple of 10. What is the probability that an error in this codeword will occur and not be detected?