Propositions

Question 1

Trivial Bound

Answer 1

If [n,k,d]_q - codes exist then k ≤ n and d ≤ n

Question 2

Let S be a syndrome map for a linear code C ⊆ F_qⁿ. If v, y ∈ F_qⁿ then

S(v) = S(y) <==> ?

S(v) = 0 <==> ?

Answer 2

Let S be a syndrome map for a linear code C ⊆ F_qⁿ. If v, y ∈ F_qⁿ then

S(v) = S(y) <==> v, y are in the same coset of C

S(v) = 0 <==> v ∈ C

Question 3

Let C₁, C₂ ⊆ F_qⁿ be two linear codes. What is d(|C₁|C₂|) ?

Answer 3

d(|C₁|C₂|) = min{2d(C₁), d(C₂)}

Question 4

R(r+1, m+1) = ?

Answer 4

R(r+1, m+1) = |R(r+1, m)|R(r, m)|