MinT - Information on Result #894718

Information on Result #894718

Linear OOA(2¹⁴⁸, 78, F₂, 2, 76) (dual of [(78, 2), 8, 77]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁷¹, 39, F₂, 2, 38) (dual of [(39, 2), 7, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁷¹, 41, F₂, 2, 38) (dual of [(41, 2), 11, 39]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2⁷², 42, F₂, 2, 39) (dual of [(42, 2), 12, 40]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(8¹⁰, 14, F₈, 9) (dual of [14, 4, 10]-code), using
        extended algebraic-geometric code AG_e(F,4P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
        F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
      2. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]
linear OOA(2⁷⁷, 39, F₂, 2, 76) (dual of [(39, 2), 1, 77]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁷⁷, 39, F₂, 2, 77) (dual of [(39, 2), 1, 78]-NRT-code), using
  - dual of repetition NRT-code with length 39 [i]

Mode: Constructive and linear.

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