9 Section 64 states that for a given positive integer t if a

9 Section 6.4 states that for a given positive integer t, if a code satisfies 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 the received sequence must be at least as close to as to w. Note: The remaining problems concern material in Appendix G

Solution

Let us consider we need positive integer if code is able to satisy dmin U 12t +12 then the code could correct all the bits erros up to and including erros of bits.
Now consider if dmin U 2t it means all errors 1t-12 bits could be corrects and the errors of t bits could be detected but we cannot say corrected.In contrary to it, any code for which all the errors having magnitude t whuch are corrected must satisfy dmin U 12t+12 and those error of magnitude 1t-12 and of magnitude must satisfy dmin U 12t+12.