Semidefinite Code Bounds Based on Quadruple Distances

Let A ( n , d ) be the maximum number of 0, 1 words of length n , any two having Hamming distance at least d . It is proved that A (20,8)=256, which implies that the quadruply shortened Golay code is optimal. Moreover, it is shown that A (18,6) ≤ 673, A (19,6) ≤ 1237, A (20,6) ≤ 2279, A (23,6) ≤ 136...

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