Probability of weight distribution of a Random Linear Code

Question

Suppose that the weight distribution of a random binary code $[n,k]-C$ ($n$ length of the code and $k$ rank/dimension of the code) follows the binomial distribution closely. In other words, the expected number of words of weight $m$, $0\leq m\leq n$, in $C$ is $2^{k−n}\binom{n}{m}$. Suppose we known there are $p$ codewords with Hamming weight $a$. Let $B$ that subset of codewords. How many choices we need to perform in $C$ to find $B$ with probability of $l$?