Reed-solomon parity check matrix

1. How do you do a parity-check matrix?
2. How is Reed-Solomon calculated?
3. How do you create a parity-check matrix for Hamming code?
4. Where is parity-check matrix in cyclic code?

How do you do a parity-check matrix?

The parity check matrix of a shortened code is obtained by removing the u columns corresponding to the removed symbols from the parity check matrix of the original code. The minimum distance of a shortened code is at least equal to the minimum distance of the original code.

How is Reed-Solomon calculated?

A Reed-Solomon codeword has 2t syndromes that depend only on errors (not on the transmitted code word). The syndromes can be calculated by substituting the 2t roots of the generator polynomial g(x) into r(x). This can be done using the Berlekamp-Massey algorithm or Euclid's algorithm.

How do you create a parity-check matrix for Hamming code?

The product C = M × G, accomplishes the codeword generation given only the four input bits M, and where modulus 2 arithmetic is assumed. A received codeword can be checked by confirming the even parity of the bits found within each circle of the Venn diagran.

Where is parity-check matrix in cyclic code?

A parity-check matrix of C may be obtained from h(x). = a(x) + xna(x). hivn−i−j = 0 for 1 ≤ j ≤ n − k. Then H is a parity-check matrix of the cyclic code C.