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Sum and product tables for Galois fields. (English) Zbl 0592.12014
Summary: This paper is concerned with the construction of sum and product tables for Galois fields GF(q) in which q is a power of a prime number p. Sufficient elementary theory is presented to provide a basis for the development of methods of representation, addition and multiplication for the field elements of GF(q). The methods are oriented towards the use of operations from the prime field GF(p) that are easy to define and implement in terms of modulo-p arithmetic. They lead to a compact form of representation for the field elements and to simply applied procedures for the construction of the sum and product tables. Examples of the methods and procedures proposed are given throughout, and sum and product tables are given for Galois fields GF(q) when q has values up to 27.
MSC:
11T55Arithmetic theory of polynomial rings over finite fields
12-04Machine computation, programs (field theory)