states that for a given positive integer t, if a code satisfies dmin 2t + 1,

states that for a given positive integer t, if a code satisfies dmin Ú 2t + 1, then the code can correct all bit errors up to and including errors of t bits. Prove this assertion. Hint: Start by observing that for a codeword w to be decoded as another codeword w, the received sequence must be at least as close to w as to w.