MinT - Information on Result #908790

Information on Result #908790

Linear OOA(2⁹⁹, 52, F₂, 2, 56) (dual of [(52, 2), 5, 57]-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(2⁸⁹, 47, F₂, 2, 51) (dual of [(47, 2), 5, 52]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁸⁹, 49, F₂, 2, 51) (dual of [(49, 2), 9, 52]-NRT-code), using
  - 2 step truncation [i] based on linear OOA(2⁹¹, 50, F₂, 2, 53) (dual of [(50, 2), 9, 54]-NRT-code), using
    - strength reduction [i] based on linear OOA(2⁹¹, 50, F₂, 2, 55) (dual of [(50, 2), 9, 56]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
        Denniston code D(1,8) [i]
        linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5 (see above)

Mode: Constructive and linear.

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