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Code fragment 2: Polynomial division with deferred message XORing. This is the standard bit-at-a-time hardware CRC implementation, and is well worthy of study; once you understand why this computes exactly the same result as the first version, the remaining optimizations are quite straightforward.
For a compact Aztec code, it is broken into four 7-bit pieces to leave room for the orientation marks. For a full Aztec code, it is broken into four 10-bit pieces, and those pieces are each divided in half by the reference grid. In some cases, the total capacity of the matrix does not divide evenly by full code words.
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
In cryptography, Lucifer was the name given to several of the earliest civilian block ciphers, developed by Horst Feistel and his colleagues at IBM.Lucifer was a direct precursor to the Data Encryption Standard.
Let H be a Hadamard matrix of order n.The transpose of H is closely related to its inverse.In fact: = where I n is the n × n identity matrix and H T is the transpose of H.To see that this is true, notice that the rows of H are all orthogonal vectors over the field of real numbers and each have length .
This power of 2 is multiplied (arithmetic modulo 2 32) by the de Bruijn sequence, thus producing a 32-bit product in which the bit sequence of the 5 MSBs is unique for each power of 2. The 5 MSBs are shifted into the LSB positions to produce a hash code in the range [0, 31], which is then used as an index into hash table BitPositionLookup.
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.
For digital video sources, the 10-bit YCbCr values for SD color bars [23] are based on the SMPTE formula for Y from the NTSC system (Y = 0.299R + 0.587G + 0.114B). [24] The following table show the expected digital values, for example when measured using a signal analyzer .