Sex-linking requires no white. It does require that the female have the dominant allele of a sex-linked gene and that the male be pure for the recessive allele of that same gene, and the gene's expression should be obvious at time of hatching. The most common gene used for creating sex-linked birds is silver: S/- hen and s+/s+ cock.
Ideally you do
NOT want either one to carry recessive or dominant white, which can mask the silver or gold. If both parents carry a single allele of recessive white, you will have some white offspring. If either is pure for recessive white, you cannot tell whether the bird is silver or gold.
Likewise if a hen carries dominant white (either one or two copies) and silver (I/? S/-), you cannot differentiate it from one that has two copies of dominant white and gold. (I/I s+/-). One copy of dominant white inhibits the expression of black pigment; a second copy inhibits the expression of red pigment. However, silver also expresses the expression of sex-linked red pigment.
With black sex-linking, the hen must be barred and the cock not-barred. Once again, you do not want white, for similar reasons. If either carry a copy of recessive white, some of the offspring will be white. If the mother carries dominant white, you cannot tell whether she is barred or not. If the father carries dominant white, you cannot determine that he is not-barred.
For barred chicks, the size of the head spot can differentiate between a bird that has one copy (females and het. males) and those that have two copies (males). With a sex-linked cross, none of the females should have
any barring, and thus will not have a head spot; if they do, the father carried a copy of barring. The males in a sex-linked cross should have ONE copy of barring, inherited from the mother.
https://www.backyardchickens.com/forum/viewtopic.php?id=261208 goes into a lot of detail about sex linking, and is pretty easy to understand. Lots of chick photos that depict male vs female, too.