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Consider the input code as 1101 1110 0001 0110 (this is the previous code with one error). We know the degree of the polynomial p x {\textstyle p_{x}} is at most r = 2 {\textstyle r=2} , we start by searching for monomial of degree 2.
Message-ID is a unique identifier for a digital message, most commonly a globally unique identifier used in email and Usenet newsgroups. [1] Message-IDs are required to have a specific format which is a subset of an email address [2] and be globally unique. No two different messages must ever have the same Message-ID.
LDPC codes have no limitations of minimum distance, [34] that indirectly means that LDPC codes may be more efficient on relatively large code rates (e.g. 3/4, 5/6, 7/8) than turbo codes. However, LDPC codes are not the complete replacement: turbo codes are the best solution at the lower code rates (e.g. 1/6, 1/3, 1/2). [35] [36]
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method.
Next, these 24 message symbols are encoded using C2 (28,24,5) Reed–Solomon code which is a shortened RS code over . This is two-error-correcting, being of minimum distance 5. This is two-error-correcting, being of minimum distance 5.
One of the original and now most common means of application checkpointing was a "save state" feature in interactive applications, in which the user of the application could save the state of all variables and other data and either continue working or exit the application and restart the application and restore the saved state at a later time.
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The QR code, Ver 3 (29×29) uses interleaved blocks. The message has 26 data bytes and is encoded using two Reed-Solomon code blocks. Each block is a (255,233) Reed Solomon code shortened to a (35,13) code. The Delsarte–Goethals–Seidel [12] theorem illustrates an example of an application of shortened Reed–Solomon codes.