Search results
Results from the WOW.Com Content Network
Let m be an odd number, and =.We first describe the extended Preparata code of length + = +: the Preparata code is then derived by deleting one position.The words of the extended code are regarded as pairs (X, Y) of 2 m-tuples, each corresponding to subsets of the finite field GF(2 m) in some fixed way.
As well as correcting some errors and adding more exercises, the third edition includes new material on connections between greedily constructed lexicographic codes and combinatorial game theory, the Griesmer bound, non-linear codes, and the Gray images of codes. [9] [10]
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.
Hadamard code is a [,,] linear code and is capable of correcting many errors. Hadamard code could be constructed column by column : the i t h {\displaystyle i^{th}} column is the bits of the binary representation of integer i {\displaystyle i} , as shown in the following example.
The distance d was usually understood to limit the error-correction capability to ⌊(d−1) / 2⌋. The Reed–Solomon code achieves this bound with equality, and can thus correct up to ⌊(n−k) / 2⌋ errors. However, this error-correction bound is not exact.
In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a Galois field). BCH codes were invented in 1959 by French mathematician Alexis Hocquenghem, and independently in 1960 by Raj Chandra Bose and D. K. Ray ...
The main idea is to choose the error-correcting bits such that the index-XOR (the XOR of all the bit positions containing a 1) is 0. We use positions 1, 10, 100, etc. (in binary) as the error-correcting bits, which guarantees it is possible to set the error-correcting bits so that the index-XOR of the whole message is 0.
In coding theory, burst error-correcting codes employ methods of correcting burst errors, which are errors that occur in many consecutive bits rather than occurring in bits independently of each other.