We study single error-correcting codes for the asymmetric channel with input and output alphabets being {0, 1,…, a — 1⩽ . From an abelian group G of order N with elements g 0 = 0, g 1 ,…, g N—1 , Constantin and Rao (1979, Inform. Contr. 40 , 20–36) define V g = {(b 1 ,b 2 ,...,b n−1 ) ∈ {O, 1,..., a − 1 } N−1 | ∑ N−1 i−1 b i g i 0 g} and show that V g correct single errors. We give explicit expressions for the size and weight distribution of these codes. We further give a short discussion of some constant weight codes obtained by a similar construction.