A table of upper bounds for binary codes
Let A(n, d) denote the maximum possible number of codewords in an (n, d) binary code. We establish four new bounds on A(n, d), namely, A(21, 4) less than or equal to 43 689, A(22, 4) less than or equal to 87 378, A(22, 6) less than or equal to 6941, and A(23, 4) less than or equal to 173 491. Furthermore, using recent upper bounds on the size of constant-weight binary codes, we reapply known methods to generate a table of bounds on A(n, d) for all n less than or equal to 28. This table extends the range of parameters compared with previously known tables.
upper bounds binary codes constant-weight codes delsarte inequalities linear programming