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If the minority is larger than the maximum number of errors possible, the decoding step fails knowing there are too many errors in the input code. Once a coefficient is computed, if it's 1, update the code to remove the monomial μ {\textstyle \mu } from the input code and continue to next monomial, in reverse order of their degree.
A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages.
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Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
A Reed–Solomon code (like any MDS code) is able to correct twice as many erasures as errors, and any combination of errors and erasures can be corrected as long as the relation 2E + S ≤ n − k is satisfied, where is the number of errors and is the number of erasures in the block.
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An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.