OurBigBook.com $£ Sponsor 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件邓家贵、低端人口、西藏骚乱

Finite field of non-prime order

As per classification of finite fields those must be of prime power order.

Video 4. "Finite fields made easy by Randell Heyman (2015)" at youtu.be/z9bTzjy4SCg?t=159 shows how for order

9 = 3 \times 3

. Basically, for order

p^{n}

, we take:

each element is a polynomial in $GF (p) [x]$ , $GF (p) [x]$ , the polynomial ring over the finite field $GF (p)$ with degree smaller than $n$ . We've just seen how to construct $GF (p)$ for prime $p$ above, so we're good there.
addition works element-wise modulo on $GF (p)$
multiplication is done modulo an irreducible polynomial of order $n$

For a worked out example, see: GF(4).

 Ancestors (8)

 Incoming links (2)