Answered: Given the codeword set 111111 000111…

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

Problem 1PE

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Question

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:

111111
000111
110001
101100
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:

001001

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