On the covering radius of a code and its subcodes

Abstract Let C 0 be a subcode of codimension i of a binary code C . We show that the covering radius ϱ ( C 0 ) of C 0 and the covering radius ϱ ( C ) of C satisfy ϱ ( C 0 )⩽ ϱ ( C )( i +1)+ i . When i  1, we determine the exact range of values for ϱ ( C 0 ) and ϱ ( C ). We also obtain an improved inequality for large i .