cyclic code in a sentence

Examples

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