7146 Coding Theory

Question:

The field GF(4) contains four elements 0-1a, b and addition and multiplication tables.

0 1 A b

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1 0 1 1 a

A 0 a B 1

b 0 and b 1

Multiplication table of GF(4)

+ 0 1 A b

0 0 1

1 1 0

b b

1) Show that the vectors V1 = (1.0,0.1,1), v2= (0.1,0.1,a), and v3 = (0.0,1,1,b). V(5,4) is linearly independent

2) Let us agree that vectors like V3 V(5,4) should be represented as [0011b], and so on.

Let C be a subspace between v1= [10011], v2= [0101a], v3= [0011b].

Make a list of all codewords C within the lexigraphic ordering given in the ordering 01

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