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The QR code system was invented in 1994, at the Denso Wave automotive products company, in Japan. The initial alternating-square design presented by the team of researchers, headed by Masahiro Hara, was influenced by the black counters and the white counters played on a Go board; the pattern of position detection was found and determined by applying the least-used ratio (1:1:3:1:1) in black ...
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The first element of a CIRC decoder is a relatively weak inner (32,28) Reed–Solomon code, shortened from a (255,251) code with 8-bit symbols. This code can correct up to 2 byte errors per 32-byte block. More importantly, it flags as erasures any uncorrectable blocks, i.e., blocks with more than 2 byte errors.
It uses a very similar syntax, but in a more consolidated way as the storage space on QR codes is limited. It's also limited in the amount of data that can be stored, not just by the standard but the size of QR codes. Example. An example of a simple vCard (from RFC 6350 of August, 2011, abbreviated):
Model 1 symbols look similar, but lack version information (the blue blocks in File:QR_Code_Structure_Example_2.svg) and alignment patterns (the smaller bull's-eye near the lower-right corner. A different sort of pattern is used for a similar purpose).
Figure 1: How the output of a single iteration of the QR or LR algorithm varies alongside its input. The basic QR algorithm can be visualized in the case where A is a positive-definite symmetric matrix. In that case, A can be depicted as an ellipse in 2 dimensions or an ellipsoid in higher dimensions. The relationship between the input to the ...
QR code is a square two-dimensional bar code. QR codes have been in use since 1994. Originally used to track products in warehouses, QR codes were designed to replace the older one-dimensional bar codes. The older bar codes just represent numbers, which can be looked up in a database and translated into something meaningful.
The BCH code with and higher has the generator polynomial. This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. It is also denoted as: (15, 1) BCH code. In fact, this code has only two codewords: 000000000000000 and 111111111111111 (a trivial repetition code ).
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