Abstract :
Let n4(k, d) be the smallest integer n, such that a quaternary linear [n, k, d]-code exists. The bounds n4(5, 21) ⩽ 32, n4(5, 30) = 43, n4(5, 32) = 46, n4(5, 36) = 51, n4(5,40) ⩽ 57, n4(5, 48) ⩽ 67, n4(5, 64) = 88, n4(5, 68) ⩽ 94, n4(5, 70) ⩽ 97, n4(5, 92) ⩽ 126, n4(5, 98) ⩽ 135, n4(5, 122) = 165, n4(5, 132) ⩽ 179, n4(5, 136) ⩽ 184, n4(5, 140) = 189, n4(5, 156) ⩽ 211, n4(5,162) = 219, n4(5, 164) ⩽ 222, n4(5, 166) ⩽ 225, n4(5, 173) ⩽ 234, n4(5, 194) = 261, n4(5, 204) = 273, n4(5, 208) = 279, n4(5, 212) = 284, n4(5, 214) = 287, n4(5, 216) = 290 and n4(5, 220) = 295 are proved. A [q4 + q2 + 1, 5, q4 − q3 + q2 − q]-code over GF(q) exists for every q.
