MinT - Information on Result #1025084

Information on Result #1025084

Linear OOA(2²⁵⁵, 90, F₂, 3, 120) (dual of [(90, 3), 15, 121]-NRT-code), using juxtaposition based on

linear OOA(2³⁶, 17, F₂, 3, 21) (dual of [(17, 3), 15, 22]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,29P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2²⁰⁴, 73, F₂, 3, 98) (dual of [(73, 3), 15, 99]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2²⁰⁴, 82, F₂, 3, 98) (dual of [(82, 3), 42, 99]-NRT-code), using
  - 2² times duplication [i] based on linear OOA(2²⁰², 82, F₂, 3, 98) (dual of [(82, 3), 44, 99]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁹⁹, 81, F₂, 3, 98) (dual of [(81, 3), 44, 99]-NRT-code), using
      - strength reduction [i] based on linear OOA(2¹⁹⁹, 81, F₂, 3, 99) (dual of [(81, 3), 44, 100]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OOA(4⁵⁹, 27, F₄, 3, 49) (dual of [(27, 3), 22, 50]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,31P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
        an explicitly constructive algebraic function field [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]

Mode: Constructive and linear.

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