I don't think that is right...
There 3 Genes for White Plumage.
S - Is the Sex-linked gene silver, as seen on light sussex. The opposite gene is gold (s) This gene only changes the "red " or "gold" parts of an E locus plumage pattern, not the black parts of those patterns.
Recessive white ('c') is the gene responsible for most white breeds of fowl. It is a mutation that simply does not function as does the normal dominant gene (C). Birds that are heterozygous for this gene (Cc) can make black pigment perfectly well, but are little less than fully efficient at gold/red pigments.
The dominant white ('I') gene is mainly found in white leghorns. It is completely dominant, being less efficient as suppressing gold/red pigment than black pigment.
As for checkered I think that term would be Pied (pi) as in the Exchequer Leghorn.
( But I don't think you aren't going to get Pied with out first adding the Mottling gene (mo) )
Chris