MinT - Information on Result #1079540

Information on Result #1079540

Linear OOA(2¹⁷⁴, 4194372, F₂, 4, 11) (dual of [(4194372, 4), 16777314, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁶, 4194305, F₂, 4, 5) (dual of [(4194305, 4), 16777174, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (41, 46, 4194305)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹²⁸, 2097186, F₂, 4, 11) (dual of [(2097186, 4), 8388616, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 36, F₂, 4, 5) (dual of [(36, 4), 132, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 12, 36)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹¹⁶, 2097150, F₂, 4, 11) (dual of [(2097150, 4), 8388484, 12]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹¹⁶, 8388600, F₂, 11) (dual of [8388600, 8388484, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹¹⁶, large, F₂, 11) (dual of [large, large−116, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Mode: Constructive and linear.

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