I found this recipe at the Marquita Farms website, located in California. They have a page dedicated to black Spanish radish recipes. They indicate that the cabbage is optional.
2-3 black Spanish radishes, scrubbed and grated
3 cups finely shredded cabbage
1 cup coarsely grated carrots, any color
1/2 cup thinly sliced green or red onion or shallots
2 tablespoons fresh lemon juice
1/2 teaspoon sugar
2 tablespoons sunflower oil
2 tablespoons finely chopped fresh parsley, cilantro, or mint leaves
In a bowl toss together the radishes, the cabbage, the carrots, the onion, the lemon juice, the sugar, the oil, the herb, and salt and pepper to taste.