For each of the following binary codes, answer all of the following questions with justification: (a) (b) (c) ● Is it linear? What is its block length, message length, and rate? What is its distance? How many errors can it detect, and how many can it correct? (To answer this question you should give the largest number of errors that the code can guarantee to detect or correct. For example a simple parity bit can detect 1 or 3 errors but cannot detect 2 errors so we would say this can detect only a single error. No calculations of probability are required.) The code with seven codewords where seven messages are encoded as follows: 0000000 0010011 0100101 0110110 1001001 101 1010 1101100 The code consisting of thirty-two codewords where each codeword consists of a 5-bit message padded with an additional bit to give ODD parity: that is, each codeword contains an odd number of 1s. For example the word 11111 would be padded with a 0 to give 111110, while 00000 would be padded with a 1 to give codeword 000001. The code consisting of eight codewords encoding as follows: 000000000 001100001 010110111 011001111 100010010 101110011 110001100 111111111 (d) The code {00000000, 01010101, 11110000, 00001111}

For each of the following binary codes, answer all of the following questions with justification: (a) (b) (c) ● Is it linear? What is its block length, message length, and rate? What is its distance? How many errors can it detect, and how many can it correct? (To answer this question you should give the largest number of errors that the code can guarantee to detect or correct. For example a simple parity bit can detect 1 or 3 errors but cannot detect 2 errors so we would say this can detect only a single error. No calculations of probability are required.) The code with seven codewords where seven messages are encoded as follows: 0000000 0010011 0100101 0110110 1001001 101 1010 1101100 The code consisting of thirty-two codewords where each codeword consists of a 5-bit message padded with an additional bit to give ODD parity: that is, each codeword contains an odd number of 1s. For example the word 11111 would be padded with a 0 to give 111110, while 00000 would be padded with a 1 to give codeword 000001. The code consisting of eight codewords encoding as follows: 000000000 001100001 010110111 011001111 100010010 101110011 110001100 111111111 (d) The code {00000000, 01010101, 11110000, 00001111}

Systems Architecture

7th Edition

ISBN:9781305080195

Author:Stephen D. Burd

Publisher:Stephen D. Burd

Chapter8: Data And Network Communication Technology

Section: Chapter Questions

Problem 41VE

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