Find the Minimum Hamming distance d for the following codes: {01010,10101,11111,00000,00010}

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
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**Problem 3: Determining the Minimum Hamming Distance**

Objective: Find the minimum Hamming distance \(d\) for the given set of binary codes:

**Code Set:**
- 01010
- 10101
- 11111
- 00000
- 00010

### Explanation:

The Hamming distance between two binary codes is the number of positions at which the corresponding bits are different. To solve this problem, calculate the Hamming distance between each pair of codes in the set and identify the smallest value obtained.

For example, consider the codes 01010 and 10101:

- Compare each corresponding bit:
  - 0 vs 1 → different
  - 1 vs 0 → different
  - 0 vs 1 → different
  - 1 vs 0 → different
  - 0 vs 1 → different

Hamming distance: 5

Repeat the process for each pair of codes to find the minimum Hamming distance.
Transcribed Image Text:**Problem 3: Determining the Minimum Hamming Distance** Objective: Find the minimum Hamming distance \(d\) for the given set of binary codes: **Code Set:** - 01010 - 10101 - 11111 - 00000 - 00010 ### Explanation: The Hamming distance between two binary codes is the number of positions at which the corresponding bits are different. To solve this problem, calculate the Hamming distance between each pair of codes in the set and identify the smallest value obtained. For example, consider the codes 01010 and 10101: - Compare each corresponding bit: - 0 vs 1 → different - 1 vs 0 → different - 0 vs 1 → different - 1 vs 0 → different - 0 vs 1 → different Hamming distance: 5 Repeat the process for each pair of codes to find the minimum Hamming distance.
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