0

i am trying to create Generator polynomial for 7 error correction code words. i don't understand how coefficients calculate. The QR code specification says to use byte-wise modulo 100011101 arithmetic (where 100011101 is a binary number that is equivalent to 285 in decimal). This means that when a number is 256 or larger, it should be XORed with 285.

In other words: 2^8 = 256 xor 285 = 29 ok. But how can i calculate 5334?

5334 xor 285 = 5579 still bigger than 256.

the answer is 122. i don't understand how we found 122 ? thank you so much.

jekyll
  • 51
  • 1
  • 10
  • 5334 is a specific number. Our generator polynomial for 7 error correction code words: x^7 +127x^6 + 5334x^5 + ... so on. XORed with 285: x^7 +127x^6 + 122x^5 + ... – jekyll Jul 10 '16 at 21:03

1 Answers1

0

Think about numbers as about polynomials from F2[X]. It means that number one can be represented by 1, number 2 is represented by x, number 3 is represented by x + 1.

Number 5334 is represented by p_5334 = x^12+x^10+x^7+x^6+x^4+x^2+x^1

Number 285 is represented by p_285 = x^8+x^4+x^3+x^2+1

You need to get the polynomial p_5334 mod p_285.

Marek Klein
  • 1,410
  • 12
  • 20