MinT - Information on Result #1115791

Information on Result #1115791

Linear OOA(2²⁴⁵, 3355534, F₂, 5, 14) (dual of [(3355534, 5), 16777425, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 5, 7) (dual of [(2097150, 5), 10485685, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
linear OOA(2¹⁸⁰, 1677767, F₂, 5, 14) (dual of [(1677767, 5), 8388655, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁹, 47, F₂, 5, 7) (dual of [(47, 5), 216, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 19, 47)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶¹, 1677720, F₂, 5, 14) (dual of [(1677720, 5), 8388439, 15]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹⁶¹, 8388600, F₂, 14) (dual of [8388600, 8388439, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

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