MinT - Information on Result #1080528

Information on Result #1080528

Linear OOA(2²⁰⁷, 62, F₂, 4, 92) (dual of [(62, 4), 41, 93]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁸⁵, 33, F₂, 4, 46) (dual of [(33, 4), 47, 47]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,85P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹²², 31, F₂, 4, 92) (dual of [(31, 4), 2, 93]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹²², 32, F₂, 4, 92) (dual of [(32, 4), 6, 93]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹⁸, 6, F₂, 4, 16) (dual of [(6, 4), 6, 17]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,7P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2⁹⁸, 26, F₂, 4, 75) (dual of [(26, 4), 6, 76]-NRT-code), using
      - 4 step truncation [i] based on linear OOA(2¹⁰², 27, F₂, 4, 79) (dual of [(27, 4), 6, 80]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
        extended Reedâ€“Solomon code RS_e(2,8) [i]
        Simplex code S(2,8) [i]
        linear OOA(2⁹, 3, F₂, 4, 9) (dual of [(3, 4), 3, 10]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;3,2) [i]

Mode: Constructive and linear.

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