MinT - Information on Result #1009913

Information on Result #1009913

Linear OOA(2¹⁴⁹, 54, F₂, 3, 74) (dual of [(54, 3), 13, 75]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁹, 27, F₂, 3, 37) (dual of [(27, 3), 12, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁶⁹, 28, F₂, 3, 37) (dual of [(28, 3), 15, 38]-NRT-code), using
  - 2¹ times duplication [i] based on linear OOA(2⁶⁸, 28, F₂, 3, 37) (dual of [(28, 3), 16, 38]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2⁶⁵, 27, F₂, 3, 37) (dual of [(27, 3), 16, 38]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OOA(4¹⁹, 9, F₄, 3, 18) (dual of [(9, 3), 8, 19]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
        linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(2⁸⁰, 27, F₂, 3, 74) (dual of [(27, 3), 1, 75]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁸⁰, 27, F₂, 3, 80) (dual of [(27, 3), 1, 81]-NRT-code), using
  - dual of repetition NRT-code with length 27 [i]

Mode: Constructive and linear.

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