MinT - Information on Result #1098309

Information on Result #1098309

Linear OOA(2¹⁵⁰, 44, F₂, 5, 50) (dual of [(44, 5), 70, 51]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁵⁰, 88, F₂, 3, 50) (dual of [(88, 3), 114, 51]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁵⁰, 88, F₂, 3, 51) (dual of [(88, 3), 114, 52]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(8²⁸, 22, F₈, 3, 25) (dual of [(22, 3), 38, 26]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8²⁸, 24, F₈, 3, 25) (dual of [(24, 3), 44, 26]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,46P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
        the Klein quartic over F₈ [i]
  2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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.