Check digit scheme airline ticket

The next four sections of this chapter wilt study the application of these number theoretic ideas to four different check digit schemes. While the first two schemes (US postal money orders and airline ticket numbers) are fairly simple, they do not fare well with regards to catching all of the types of errors listed in Table 1.2. The last two schemes (UPC and ISBN) are nnore sophisticated and do a better job in catching errors. 

Suppose that the following two numbers are airline ticket identification numbers. Using the airline ticket check digit scheme, determine which is a valid number and... 

The number 0-037-1222494315 is used to identify an airplane ticket. Use the airline ticket check digit scheme to assign a check digit to this number. Be sure to identify the check digit and then to write out the entire document number. 

Comparison. You are employed by an organization that wants to adopt a check digit scheme. Your Job is to write a report called a feasibility study, in which you recommend to the company either the US postal order scheme or the airline ticket scheme. To do this, compare the US postal order check digit scheme with the airline ticket check digit scheme, paying attention to the following factors ... 

Identification numbers, and the check digit schemes that detect when these numbers have been transmitted inconectly, are crucial for the quick storage, retrieval, and transfer of vast amounts of information. In this book, a variety of check digit schemes are discussed. Gieck digit schemes vary in their ability to catch errors. Some, such as the airline ticket scheme, do not catch every occurrence of the most connnon type of error, while others, such as the ISBN scheme, catch most error patterns. Consequently, criteria for judging the reliability of check digit schemes are a central concern of this book. 

Since airline ticket numbers are large, the exercise will be completed with much smaller four-digit numbers, ai 020304. The scheme works in the same manner. The check digit 04 is appended to the three-digit number 010303 to create the identification number 01030304 such that 04 satisfies the equation 04 = 010303 (mod 7). These numbers are easier to work with, but the mathematical concept is the same. 

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