“…The number 2 is a generator of Z * 13 . By Theorem 4.4, the set X = (1, 2 2·2 , 2 2·1 ), (1, 2 2·1 , 2 2·2 ), (1, 2 2·5 , 2 2·3 ), (1, 2 2·3 , 2 2·5 ) = { (1,3,4), (1,4,3), (1,10,12), (1,12,10)} is a short covering of 2 · 12 = 24 elements of E. Since |E| = 30, we need to cover 6 remaining vectors of E. By Fact 1 of Lemma 5.5, these six vectors are: (1, 2, 11), (1,5,8), (1,6,7), (1,7,6), (1,8,5), (1,11,2). They are covered by (1,2 2·4 , −2 2·4 ) = (1, 9, 4).…”