MinT - Information on Result #1143278

Information on Result #1143278

Linear OOA(2¹²⁸, 1677765, F₂, 6, 10) (dual of [(1677765, 6), 10066462, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹³, 45, F₂, 6, 5) (dual of [(45, 6), 257, 6]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(2¹³, 45, F₂, 5, 5) (dual of [(45, 5), 212, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(2¹³, 45, F₂, 4, 5) (dual of [(45, 4), 167, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (8, 13, 45)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2¹¹⁵, 1677720, F₂, 6, 10) (dual of [(1677720, 6), 10066205, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2¹¹⁵, 8388600, F₂, 10) (dual of [8388600, 8388485, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹¹⁵, large, F₂, 10) (dual of [large, large−115, 11]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

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