property galois.ReedSolomon.c : int

The first consecutive power $$c$$ of $$\alpha$$ that defines the roots $$\alpha^c, \dots, \alpha^{c+d-2}$$ of the generator polynomial $$g(x)$$.

Examples

Construct a narrow-sense $$\textrm{RS}(15, 9)$$ code over $$\mathrm{GF}(2^4)$$ with first consecutive root $$\alpha$$.

In [1]: rs = galois.ReedSolomon(15, 9); rs
Out[1]: <Reed-Solomon Code: [15, 9, 7] over GF(2^4)>

In [2]: rs.c
Out[2]: 1

In [3]: rs.roots[0] == rs.alpha ** rs.c
Out[3]: True

In [4]: rs.generator_poly
Out[4]: Poly(x^6 + 7x^5 + 9x^4 + 3x^3 + 12x^2 + 10x + 12, GF(2^4))


Construct a narrow-sense $$\textrm{RS}(15, 9)$$ code over $$\mathrm{GF}(2^4)$$ with first consecutive root $$\alpha^3$$. Notice the design distance is the same, however the generator polynomial is different.

In [5]: rs = galois.ReedSolomon(15, 9, c=3); rs
Out[5]: <Reed-Solomon Code: [15, 9, 7] over GF(2^4)>

In [6]: rs.c
Out[6]: 3

In [7]: rs.roots[0] == rs.alpha ** rs.c
Out[7]: True

In [8]: rs.generator_poly
Out[8]: Poly(x^6 + 15x^5 + 8x^4 + 7x^3 + 9x^2 + 3x + 8, GF(2^4))