uist 'Certain Factors affecting telegraph speed' 1924). Taking this small but significant proviso into account binary numbers can be used to deliver sensitivity. For example, considering Table 3.1, moving the 1 further away from a 0 implies an increase in distance which implies an increase in sensitivity. The greater the distance between two strings of numbers (code streams in CDMA), the better the selectivity between users. The two codes shown in Table 3.2 differ in 10 places, which describes their 'hamming distance'3 from each other. If two code streams are identical (no distance between them) they can be used to lock on to each other, for example to provide a time reference from a base station to a handset or handset to a base station. Longer strings of Os and 1s will produce distinct spectral components in the frequency domain that can be used to provide a frequency reference. An example is given in Table 3.3. We can also use binary numbers as a counting system. Interestingly, as we shall see later, if we start arranging Os and 1s in a symmetric matrix of rows and columns, the binary product (sometimes known as the dot product) of the numbers in a column or row can be used to uniquely identify the position of that column or row. This is the property (described earlier) known as sequency and is the basis of many of the error coding and correction schemes used in present radio systems. Table 3.2 Coding distance - selectivity Coding distance - selectivity 01101011010010100 10011011101100010 3 Named after Richard Hamming who published a seminal paper on error coding in 1920. Interrelationship of the Physical Layer with Other Layers of the OSI Model Table 3.3 Coding distance - stability Coding distance - stability (code correlation) 01101011010010100 01101011010010100 3.3.1 Coding Distance and Bandwidth Gain A first step to increasing the distance between a 0 and a 1 is to change a 0 into a - 1 and a 1 into a +1. If we take either a -1 or a +1 and multiply by a series of - 1s and +1s running at a faster rate then 