MinT - Information on Result #1175703

Information on Result #1175703

Linear OOA(2²³⁹, 2396768, F₂, 8, 15) (dual of [(2396768, 8), 19173905, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 8, 7) (dual of [(2097150, 8), 16777135, 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(2¹⁷⁴, 1198384, F₂, 8, 15) (dual of [(1198384, 8), 9586898, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 13, F₂, 8, 7) (dual of [(13, 8), 92, 8]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(2¹², 13, F₂, 7, 7) (dual of [(13, 7), 79, 8]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹², 13, F₂, 6, 7) (dual of [(13, 6), 66, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 12, 13)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶², 1198371, F₂, 8, 15) (dual of [(1198371, 8), 9586806, 16]-NRT-code), using
    - OOA 7-folding and stacking with additional row [i] based on linear OA(2¹⁶², 8388598, F₂, 15) (dual of [8388598, 8388436, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

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