Confirming a proof on code theory:both english and math

[Lali1]

I was asked to prove a proposition about error correcting linear Code, the propositionn was:

Proposition. The covering radius of the linear code C is equal to the maximum weight of a coset leader.

It's clear that I needed to answer this question in english so I tried and here's my result:


The coset of the word -x consists of the sum of -x with each individual codeword of C, so the weights of the coset members give the distances of x from the various codewords. The minimal such weight is thus the distance of x from the code and also the weight of a coset leader. The maximum weight of a coset leader is therefore the largest distance of any word x from the code.

I'm not sure if the proof is right so I'd like to get a confirmation and as well tell me if it is easy to understand, I mean if the way I explained it in english is good.

[tulip]

I would not use "minimal" but "minimum", as to the rest it is quite clear, in my opinion. bye.