Linear Programming Bounds for Codes of Small Size

Combining linear programming approach with the Plotkin-Johnson argument for constant weight codes, we derive upper bounds on the size of codes of length n and minimum distance d = (n j)=2, 0 < j < n 1=3 . For j = o(n 1=3 ) these bounds practically coincide (are slightly better) with the Tietav ainen bound. For xed j and j proportional to n 1=3 , j < n 1=3 (2=9) lnn, it improves on the earlier known results.