MinT - Information on Result #894829

Information on Result #894829

Linear OOA(2²⁴², 126, F₂, 2, 123) (dual of [(126, 2), 10, 124]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹¹⁷, 63, F₂, 2, 61) (dual of [(63, 2), 9, 62]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹¹⁷, 64, F₂, 2, 61) (dual of [(64, 2), 11, 62]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2¹¹⁸, 65, F₂, 2, 62) (dual of [(65, 2), 12, 63]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(8⁹, 13, F₈, 8) (dual of [13, 4, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁹, 14, F₈, 8) (dual of [14, 5, 9]-code), using
        extended algebraic-geometric code AG_e(F,5P) [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(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, using
        an explicitly constructive algebraic function field [i]
linear OOA(2¹²⁵, 63, F₂, 2, 123) (dual of [(63, 2), 1, 124]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹²⁵, 63, F₂, 2, 125) (dual of [(63, 2), 1, 126]-NRT-code), using
  - dual of repetition NRT-code with length 63 [i]

Mode: Constructive and linear.

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