Error-Correcting Codes: An Application of Geometry
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چکیده
Information is stored and exchanged in the form of streams of characters from some alphabet. An alphabet is a finite set of symbols, such as the lower-case Roman alphabet {a,b,c,...,z}. Larger digits may be formed by including the upper-case Roman letters, punctuation marks, the digits 0 through 9, and possibly other symbols such as ‘$’, ‘%’, etc. In the other extreme, we may choose the simplest possible alphabet, the binary alphabet {0,1}. We prefer the binary alphabet for several reasons:
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