MinT - Information on Result #1079357

Information on Result #1079357

Linear OOA(2¹⁴⁴, 4194324, F₂, 4, 9) (dual of [(4194324, 4), 16777152, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴², 2097151, F₂, 4, 4) (dual of [(2097151, 4), 8388562, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁴², 2097151, F₂, 3, 4) (dual of [(2097151, 3), 6291411, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (38, 42, 2097151)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁰², 2097173, F₂, 4, 9) (dual of [(2097173, 4), 8388590, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 23, F₂, 4, 4) (dual of [(23, 4), 83, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁹, 23, F₂, 3, 4) (dual of [(23, 3), 60, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (5, 9, 23)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2⁹³, 2097150, F₂, 4, 9) (dual of [(2097150, 4), 8388507, 10]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2⁹³, 8388600, F₂, 9) (dual of [8388600, 8388507, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁹³, large, F₂, 9) (dual of [large, large−93, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

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