When transmitting data on a BSC with crossover probability 0 < p < 1/2 how should we decide between the [7,4,3] Hamming code and the [15,11,3] Hamming code? (a) Prove that the block error probability of the shorter code is always better to use (b) Why might we still choose to use the longer code?
When transmitting data on a BSC with crossover probability 0 < p < 1/2
how should we decide between the [7,4,3] Hamming code and the [15,11,3]
Hamming code?
(a) Prove that the block error probability of the shorter code is always
better to use
(b) Why might we still choose to use the longer code?
(1)
In the Cipher table, in the first row there are 26 English alphabets in order. Then the next row starts with the letter that has been shifted one place from the row above it.
Hence, if row 1- A B C D,
Row 2 shall be B C D E
If we keep on doing this , we shall receive something like this which is as follows:
- A B C D
- B C D E
- C D E F
- D E F G
- E F G H
- F G H I
- G H I J
- H I J K
- I J K L
- J K L M
- K L M N
- L M N O
- M N O P
- N O P Q
- P Q R
- P Q R S
- Q R S T
- R S T U
- S T U V
- T U V W
- U V W X
- V W X Y
- W X Y Z
So here we get 23 possibilities for coding English alphabets according to Vigenere cipher.
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