MinT - Information on Result #1009969

Information on Result #1009969

Linear OOA(2¹⁵⁰, 54, F₂, 3, 79) (dual of [(54, 3), 12, 80]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁷⁰, 27, F₂, 3, 39) (dual of [(27, 3), 11, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁷⁰, 28, F₂, 3, 39) (dual of [(28, 3), 14, 40]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2⁶⁷, 27, F₂, 3, 39) (dual of [(27, 3), 14, 40]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OOA(4²⁰, 9, F₄, 3, 19) (dual of [(9, 3), 7, 20]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
      2. 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, 79) (dual of [(27, 3), 1, 80]-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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