MinT - Information on Result #1056178

Information on Result #1056178

Linear OOA(2¹⁸⁸, 80, F₂, 4, 58) (dual of [(80, 4), 132, 59]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁸⁸, 160, F₂, 2, 58) (dual of [(160, 2), 132, 59]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁸⁸, 160, F₂, 2, 59) (dual of [(160, 2), 132, 60]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(16³¹, 32, F₁₆, 2, 29) (dual of [(32, 2), 33, 30]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16³¹, 33, F₁₆, 2, 29) (dual of [(33, 2), 35, 30]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,36P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
        a function field by SÃ©mirat [i]
  2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.