Abstract
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)lnn,it improves on the earlier known results.
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