EE4253 Addition and Multiplication Tables in Galois Fields


	ECE4253 Digital Communications

	Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

Addition and Multiplication Tables in Galois Fields GF(2^m)

See GF(2^m) calculator tool.

Using the Galois Field GF(2⁴) = GF(16) based on the primitive P(x) = x⁴ + x³ + 1 = (11001) = 25 (decimal)

Multiplication Table

×	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
2	2	4	6	8	10	12	14	9	11	13	15	1	3	5	7
3	3	6	5	12	15	10	9	1	2	7	4	13	14	11	8
4	4	8	12	9	13	1	5	11	15	3	7	2	6	10	14
5	5	10	15	13	8	7	2	3	6	9	12	14	11	4	1
6	6	12	10	1	7	13	11	2	4	14	8	3	5	15	9
7	7	14	9	5	2	11	12	10	13	4	3	15	8	1	6
8	8	9	1	11	3	2	10	15	7	6	14	4	12	13	5
9	9	11	2	15	6	4	13	7	14	12	5	8	1	3	10
10	10	13	7	3	9	14	4	6	12	11	1	5	15	8	2
11	11	15	4	7	12	8	3	14	5	1	10	9	2	6	13
12	12	1	13	2	14	3	15	4	8	5	9	6	10	7	11
13	13	3	14	6	11	5	8	12	1	15	2	10	7	9	4
14	14	5	11	10	4	15	1	13	3	8	6	7	9	2	12
15	15	7	8	14	1	9	6	5	10	2	13	11	4	12	3

Select a primitive polynomial P(x)

Model C-162 GALOIS FIELD MATH TABLE GENERATOR


2024-04-26 02:04:07 ADT Last Updated: 2011-02-02	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...