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Matrix Representation of Finite Fields

1994; Taylor & Francis; Volume: 67; Issue: 4 Linguagem: Inglês

10.1080/0025570x.1994.11996233

1930-0980

William P. Wardlaw,

Cellular Automata and Applications

Abstract : Finite fields (also called Galois Fields) have been studied since their introduction by Evariste Galois in 1832 and the publication of his work in 1846. In the last few decades, finite fields have become important to information theory, coding theory, and cryptography. This report presents a simple method for representing a finite field in terms of powers of a single matrix over the integers modulo the characteristic of the field. The addition and multiplication in the field are immediately obtained as the results of ordinary matrix addition and multiplication. This representation called the canonical cyclic representation, makes it easy to understand the field structure and to carry out computations in the field.