Quasi-perfect linear codes with minimum distance 4

Some new infinite families of short quasi-perfect linear codes are described. Such codes provide improvements on the currently known upper bounds on the minimal length of a quasi-perfect [n, n - m, 4](q)-code when either 1) q = 16, m >= 5, in odd, or 2) q = 2(i), 7 <= i <= 15, m >= 4, or 3) q 2(2l), l >= 8, m >= 5; m, odd. As quasi-perfect [n, n - m, 4](q)-codes and complete n-caps in projective spaces PG(m. - 1, q) are equivalent objects, new upper bounds on the size of the smallest complete cap in PG(m - 1, q) are obtained.