MinT - Information on Result #1010178

Information on Result #1010178

Linear OOA(2²¹⁸, 78, F₂, 3, 103) (dual of [(78, 3), 16, 104]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰², 39, F₂, 3, 51) (dual of [(39, 3), 15, 52]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁰², 43, F₂, 3, 51) (dual of [(43, 3), 27, 52]-NRT-code), using
  - 2¹ times duplication [i] based on linear OOA(2¹⁰¹, 43, F₂, 3, 51) (dual of [(43, 3), 28, 52]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2⁹⁸, 42, F₂, 3, 51) (dual of [(42, 3), 28, 52]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OOA(4²⁸, 14, F₄, 3, 25) (dual of [(14, 3), 14, 26]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,16P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, 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]
linear OOA(2¹¹⁶, 39, F₂, 3, 103) (dual of [(39, 3), 1, 104]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹¹⁶, 39, F₂, 3, 116) (dual of [(39, 3), 1, 117]-NRT-code), using
  - dual of repetition NRT-code with length 39 [i]

Mode: Constructive and linear.

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