MinT - Information on Result #908794

Information on Result #908794

Linear OOA(2¹¹⁵, 60, F₂, 2, 65) (dual of [(60, 2), 5, 66]-NRT-code), using juxtaposition based on

linear OOA(2⁵, 5, F₂, 2, 4) (dual of [(5, 2), 5, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁰⁵, 55, F₂, 2, 60) (dual of [(55, 2), 5, 61]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁰⁵, 56, F₂, 2, 60) (dual of [(56, 2), 7, 61]-NRT-code), using
  - strength reduction [i] based on linear OOA(2¹⁰⁵, 56, F₂, 2, 62) (dual of [(56, 2), 7, 63]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2⁷, 7, F₂, 2, 5) (dual of [(7, 2), 7, 6]-NRT-code), using
        extracting embedded OOA [i] based on digital (2, 7, 7)-net over F₂, using
        a shift-net [i]
      2. linear OOA(2⁹¹, 49, F₂, 2, 56) (dual of [(49, 2), 7, 57]-NRT-code), using
        3 step truncation [i] based on linear OOA(2⁹⁴, 51, F₂, 2, 59) (dual of [(51, 2), 8, 60]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
        projective code from ovoid in PG(3,Â 4) [i]
        linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [i]

Mode: Constructive and linear.

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