However cyclic codes can indeed detect " most " bursts of length > r.
12.
If the dropped symbols are not check symbols then this cyclic code is also a shortened code.
13.
Cyclic codes can also be used to correct double errors over the field GF ( 2 ).
14.
The codewords of this cyclic code are all the polynomials that are divisible by this generator polynomial.
15.
Cyclic codes can detect all bursts of length up to \ ell = n-k = r.
16.
Every cyclic code with generator polynomial of degree r can detect all bursts of length \ leqslant r.
17.
Thus, the Fire Code above is a cyclic code capable of correcting any burst of length 5 or less.
18.
Their structure is strongly related to Galois fields because of which the encoding and decoding algorithms for cyclic codes are computationally efficient.
19.
Cyclic codes are defined as follows : think of the q symbols as elements in \ mathbb { F } _ q.
20.
Cyclic codes can be used to correct errors, like Hamming codes as a cyclic codes can be used for correcting single error.
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