Cyclic codes can be used to correct errors, like Hamming codes as a cyclic codes can be used for correcting single error.
22.
Any cyclic code can be converted to quasi-cyclic codes by dropping every b th symbol where b is a factor of n.
23.
Any cyclic code can be converted to quasi-cyclic codes by dropping every b th symbol where b is a factor of n.
24.
Although this definition is sufficient to describe what a burst error is, the majority of the tools developed for burst error correction rely on cyclic codes.
25.
To convert ( n, k ) cyclic code to ( n-b, k-b ) shortened code, set b symbols to zero and drop them from each codeword.
26.
Before delving into the details of cyclic codes first we will discuss quasi-cyclic and shortened codes which are closely related to the cyclic codes and they all can be converted into each other.
27.
Before delving into the details of cyclic codes first we will discuss quasi-cyclic and shortened codes which are closely related to the cyclic codes and they all can be converted into each other.
28.
An [ n, k ] linear code is called a " proper shortened cyclic code " if it can be obtained by deleting b positions from an ( n + b, k + b ) cyclic code.
29.
An [ n, k ] linear code is called a " proper shortened cyclic code " if it can be obtained by deleting b positions from an ( n + b, k + b ) cyclic code.
30.
So, cyclic codes are vectors in the field GF ( q ) and the spectrum given by its inverse fourier transform is over the field GF ( q ^ m ) and are constrained to be zero at certain components.
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