Question

Let f:Z₂₆​ →Z₂₆ and f(x)=9x+2mod26 be an encoding function. Encode "ABSTRACT ALGEBRA".

Answer 1

To encode 'ABSTRACT ALGEBRA' using the function f(x) = 9x + 2 mod 26, each letter is first converted to its position in the alphabet, the function is applied, and the resulting numbers are translated back into letters.

Step-by-step explanation:

The process of encoding the message "ABSTRACT ALGEBRA" using the given function f(x) = 9x + 2 mod 26 involves converting each letter to its respective position in the alphabet (A=1, B=2, ..., Z=26), applying the function to these numeric values, and then converting the numeric results back to letters.

First, the message is converted to numbers: A=1, B=2, C=3, T=20, R=18, A=1, C=3, T=20, A=1, L=12, G=7, E=5, B=2, R=18, A=1.

Then, each number is encoded using the function: For example, encoding A (which is 1) gives f(1) = 9(1) + 2 mod 26, which equals 11 mod 26 (K).

The entire message can be encoded this way, and the resulting numeric values are then mapped back to their corresponding letters to obtain the encoded message.