Question

PARITY CHECK MATRIX DECODING 1. The affine cipher y 21x + 11 (mod 26) was used to encode a message. Each resulting letter of the ciphertext was converted to the five-bit string consisting of the base-two equivalent of the value of the letter. The systematic (9,5) linear code with standard generator matrix G given by [1 0 0 0 0 1 0 0 11 To 1000 1100l G= 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 was then used to send the message. Each codeword that was transmitted had at most one error when it was received. The following bit stream was received. 1000001100001011100011100110010001111000001101000101011 01100110000011100101111100 Find the message. (Spacing between words is required; punctuation is optional but appreciated.) Find the digit in the hundredths place pf the square root of the number in the message. (No numbers-spell the answer.) Encode the digit using the same affine cipher that was used to encode the original message. • Using the same standard generator matrix G, determine the sequence of codewords to be sent; separate the codewords with commas.

Answer 1

The given problem : The raffine Cipher Yetset 19 (mod 26) was used rencode message 9. Each ciphertent Convent into five bit string to the binary equivalent number ro0007110017 generatá matric Galo 1000 1 1 00 OU 100 111 TO0010 Ili Ilo to OOOTI O OD 1 bs bit equivalent binary number Yagu ta l'uod db) G-19 Cuod 26) = 72 7²84-19cunod 26]=4 . 71 [y-la)= 1988-19].) iay- 19 – 197-(4-19) € 19y-(-7)(-19) § 19.4 + 7 x 19 (133)s will be converted a 198 +133- v into 3 mod > 0 in & bit equivalent. c) 19 y + 3 mod. number 8 = 199+3 mot 26