MinT - Information on Result #1079263

Information on Result #1079263

Linear OOA(2¹⁴⁰, 4194308, F₂, 4, 8) (dual of [(4194308, 4), 16777092, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴³, 2097153, F₂, 4, 4) (dual of [(2097153, 4), 8388569, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁴³, 2097153, F₂, 3, 4) (dual of [(2097153, 3), 6291416, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (39, 43, 2097153)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2⁹⁷, 2097155, F₂, 4, 8) (dual of [(2097155, 4), 8388523, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵, 5, F₂, 4, 4) (dual of [(5, 4), 15, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁵, 5, F₂, 3, 4) (dual of [(5, 3), 10, 5]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁹², 2097150, F₂, 4, 8) (dual of [(2097150, 4), 8388508, 9]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2⁹², 8388600, F₂, 8) (dual of [8388600, 8388508, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁹², large, F₂, 8) (dual of [large, large−92, 9]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

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