I posted this question in http://math.stackexchange.com/questions/1142698/picking-codewords-that-are-close a week back.

Let $[n,k,d]$ be a linear code over $\Bbb F_q$ with minimum distance $d$ and number of minimum weight codewords $N_d$.

How many ways can you select codewords $c_1,\dots,c_T$ (assume $T\ll q^k$) such that there are two non-equal codewords in collection at a distance $d$ from each other ($c_i\neq c_j$, $|c_i-c_j|=d$)?

Presumably answer is $2^{\lambda T}$. If so what is correct estimate to $\lambda$?

Atleast could we say something when code is MDS (cases where weight enumerators known).

I posted this question in https://math.stackexchange.com/questions/1142698/picking-codewords-that-are-close a week back.

Let $[n,k,d]$ be a linear code over $\Bbb F_q$ with minimum distance $d$ and number of minimum weight codewords $N_d$.

How many ways can you select codewords $c_1,\dots,c_T$ (assume $T\ll q^k$) such that there are two non-equal codewords in collection at a distance $d$ from each other ($c_i\neq c_j$, $|c_i-c_j|=d$)?

Presumably answer is $2^{\lambda T}$. If so what is correct estimate to $\lambda$?

Atleast could we say something when code is MDS (cases where weight enumerators known).