Linear Programming Bounds for Codes of Small Size

Combining linear programming with the Plotkin–Johnson argument for constant weight codes, we derive upper bounds on the size of codes of lengthnand minimum distanced=(n − j) /2, 0<j<n1/3.Forj=o(n1/3)these bounds practically coincide with (are slightly better than) the Tietäväinen bound. Forjfixed and forjproportional ton1/3, j<n1/3-(2 /9)ln n,it improves on the earlier known results.