Semidefinite Code Bounds Based on Quadruple Distances

  title={Semidefinite Code Bounds Based on Quadruple Distances},
  author={Dion Gijswijt and Hans D. Mittelmann and Alexander Schrijver},
  journal={IEEE Transactions on Information Theory},
Let <i>A</i>(<i>n</i>,<i>d</i>) be the maximum number of 0, 1 words of length <i>n</i> , any two having Hamming distance at least <i>d</i>. It is proved that <i>A</i>(20,8)=256, which implies that the quadruply shortened Golay code is optimal. Moreover, it is shown that <i>A</i>(18,6) ≤ 673, <i>A</i>(19,6) ≤ 1237, <i>A</i>(20,6) ≤ 2279, <i>A</i>(23,6) ≤ 13674, <i>A</i>(19,8) ≤ 135, <i>A</i>(25,8) ≤ 5421, <i>A</i>(26,8) ≤ 9275, <i>A</i>(27,8) ≤ 17099, <i>A</i>(21,10) ≤ 47, <i>A</i>(22,10) ≤ 84… 

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