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2. Mathematics of cyclic redundancy checks - Wikipedia

   en.wikipedia.org/wiki/Mathematics_of_cyclic...

   All the well-known CRC generator polynomials of degree have two common hexadecimal representations. In both cases, the coefficient of x n {\displaystyle x^{n}} is omitted and understood to be 1. The msbit-first representation is a hexadecimal number with n {\displaystyle n} bits, the least significant bit of which is always 1.

3. Cyclic redundancy check - Wikipedia

   en.wikipedia.org/wiki/Cyclic_redundancy_check

   To compute an n-bit binary CRC, line the bits representing the input in a row, and position the (n + 1)-bit pattern representing the CRC's divisor (called a "polynomial") underneath the left end of the row. In this example, we shall encode 14 bits of message with a 3-bit CRC, with a polynomial x 3 + x + 1.

4. Computation of cyclic redundancy checks - Wikipedia

   en.wikipedia.org/wiki/Computation_of_cyclic...

   When implemented in bit serial hardware, the generator polynomial uniquely describes the bit assignment; the first bit transmitted is always the coefficient of the highest power of , and the last bits transmitted are the CRC remainder (), starting with the coefficient of and ending with the coefficient of , a.k.a. the coefficient of 1.

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6. Error correction code - Wikipedia

   en.wikipedia.org/wiki/Error_correction_code

   The fundamental principle of ECC is to add redundant bits in order to help the decoder to find out the true message that was encoded by the transmitter. The code-rate of a given ECC system is defined as the ratio between the number of information bits and the total number of bits (i.e., information plus redundancy bits) in a given communication ...

7. Error detection and correction - Wikipedia

   en.wikipedia.org/wiki/Error_detection_and_correction

   It is not suitable for detecting maliciously introduced errors. It is characterized by specification of a generator polynomial, which is used as the divisor in a polynomial long division over a finite field, taking the input data as the dividend. The remainder becomes the result. A CRC has properties that make it well suited for detecting burst ...