Given the codeword set 111111 000111 110001 101100 011010  Add another codeword to this set that has distance at least 3 to all other codewords

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Given the codeword set 111111 000111 110001 101100 011010 
Add another codeword to this set that has distance at least 3 to all other codewords.

Expert Solution
Step 1: Introduction

To add a codeword to the set with a minimum distance of 3 to all other codewords, we need to ensure that the Hamming distance between the new codeword and all existing codewords is at least 3. The Hamming distance is the number of positions at which two codewords differ.

Let's consider the existing codewords:

  1. 111111
  2. 000111
  3. 110001
  4. 101100
  5. 011010

To create a new codeword with a minimum distance of 3 to all of these, we can choose a codeword that differs in at least 3 positions from each of them. Here's one such example:

  1. 001001
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