Block codes - Codes and Turbo Codes - page 166

Example 3

Some calculations in field F 16 are given in table 4.11 for addition, in table 4.12
for multiplication and in table 4.13 for division.

α 2 α 4

+

α 8 0011 + 0101 = 0110 = α 5 0100 + 0101 = 0001 = 1

α 10 0100 + 0111 = 0011 = α 4 0011 + 0111 = 0100 = α 2

Table 4.11 - Addition in F 16

α 2 α 6

×

α 8 α 10 α 14

α 14 α 16 = α as α 15 =1 α 20 = α 5 as α 15 =1

Table 4.12 - Multiplication in F 16

÷ α 2 α 12

α 8 α − 6 = α 9 as α 15 =1 α 4

α 14 α − 12 = α 3 as α 15 =1 α − 2 = α 13 as α 15 =1

Table 4.13 - Division in F 16