Simple Linear Codes/Algebra Question

[yellowjack]

I'm surprised to see the lack of math questions in this forum, so I'll be cross-posting in the Probability forum to hopefully get an answer.

Suppose v_1 is one of the code words in the basis for C where q=2, n=4, and M = 4

v_1 = (0 0 1 1)

What is 2*(0 0 1 1)?
(This will solve why I get c_1*v_1 + c_2*v_2 + c_3*v_3 = 0 for c_1 = c_2 = c_3 = 2, which is incorrect)

[pzhon]

Are we supposed to guess what all of the notation means?

Ok, my guess is that q=2 means your scalar field has size 2 hence characteristic 2, which means 2 times any vector is the 0 vector.

[yellowjack]

yes, sorry
q = 2 (binary code)
n = length of word
M = number of words in code

[pzhon]

2*v1=(0,0,0,0). That's trivial, since 2=0 in your scalar field.

You're looking for a nontrivial linear dependence between v1, v2, and v3, which should exist because the code is 2-dimensional. There are only two choices for each coefficient, 0 and 1, so there are only 8 linear combinations of v1, v2, and v3. All but one linear combination should be ruled out immediately, and that last one works.

[yellowjack]

Awesome, I was about to post since I figured out c=0,1 only for q=2.

Thanks /images/graemlins/smile.gif