weight distribution hamming radius
The covering radius of C is deï¬ned as r(C)=max xâF min yâC+x wt(x), where wt(Â·) denotes the Hamming weight. Bounding the covering radius of codes is one of the main extremal problems of coding theory. Let C ={x â F: (x,c)=0 âc âC} be the dual code of C and (A i,0 â¤i â¤n) be its weight distribution, where A i =|{x âC: wt(x)=i}|and (x,c)denotes the dot product.