Other Aztec Code - how to construct a generator polynomial

Johan Schoeman

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The construction of Reed Solomon generator polynomials for Aztec codes are very similar to that of QR Codes (See http://www.b4x.com/android/forum/th...uct-a-generator-polynomial.43290/#post-263423 for QR Code generator polynomials). Some minor differences between generator polynomials of QR Codes and that of Aztec Codes. Amongst others is the fact that Aztec codes have different generator polynomials for the mode message and the data message. The prime polynomial(s) is also different to that of QR Codes (285 decimal for QR Codes, 19 decimal for Aztec Code mode messages and 67 decimal, 301 decimal, 1033 decimal, and 4201 decimal for Aztec code data messages, depending on the Aztec code layers i.e Layer 1 to Layer 32).

Attached project caters for gf(256) with a prime polynomial of 301decimal that is required for layer 3 to layer 8 Aztec codes data messages. Code in the attached project needs to be changed slightly to accommodate the different requirements of Aztec Codes wrt mode message and data messages based on the layer level. All of the changes to the code can be done by taking the below into consideration:

Set up the log / anti-log tables for GF(x)
gf = 16 for the mode message with prime polynomial x^4 + x + 1 = decimal 19
gf = 64 for layers 1 to 2 with prime polynomial x^6 + x + 1 = decimal 67
gf = 256 for layers 3 to 8 with prime polynomial x^8 + x^5 + x^3 + x^2 + 1 = decimal 301
gf = 1024 for layers 9 to 22 with prime polynomial x^10 + x^3 + 1 = decimal 1033
gf = 4094 for layers 23 to 32 with prime polynomial x^12 + x^6 + x^5 + x^3 + 1 = decimal 4201

gf =>> means Galios Field
 

Attachments

  • AztecRSGeneratorPolynomialV1.zip
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