MinT - Information on Result #1079445

Information on Result #1079445

Linear OOA(2¹⁶⁸, 4194317, F₂, 4, 10) (dual of [(4194317, 4), 16777100, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁴, 2097153, F₂, 4, 5) (dual of [(2097153, 4), 8388568, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (39, 44, 2097153)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹²⁴, 2097164, F₂, 4, 10) (dual of [(2097164, 4), 8388532, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 14, F₂, 4, 5) (dual of [(14, 4), 47, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 9, 14)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹¹⁵, 2097150, F₂, 4, 10) (dual of [(2097150, 4), 8388485, 11]-NRT-code), using
    - OOA 4-folding [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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