MinT - Information on Result #1079281

Information on Result #1079281

Linear OOA(2¹⁵¹, 4194598, F₂, 4, 8) (dual of [(4194598, 4), 16778241, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁴, 4194305, F₂, 4, 4) (dual of [(4194305, 4), 16777176, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁴⁴, 4194305, F₂, 3, 4) (dual of [(4194305, 3), 12582871, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (40, 44, 4194305)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁰⁷, 2097299, F₂, 4, 8) (dual of [(2097299, 4), 8389089, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁵, 149, F₂, 4, 4) (dual of [(149, 4), 581, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁵, 149, F₂, 3, 4) (dual of [(149, 3), 432, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (11, 15, 149)-net over F₂, using
        linear code embedding found in a computer search [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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