Decimal Codes
نویسنده
چکیده
To make error correcting codes easier to use and analyze, it is necessary to impose some algebraic structure on them. It is especially useful to have an alphabet in which it is possible to add, subtract, multiply and divide without restriction. In other words we wish to construct a finite field. Evarist Galois (1811-32), a French mathematician who died in a duel at the age of 20 introduced finite fields and proved that there exists a field of order q if and only if q is a prime power (i.e. q = pr, where p is prime and r is a positive integer). Furthermore, there is, up to relabeling, only one field of that order. Finite fields of order q are also known as Galois field of order q and are denoted by GF (q).
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