MinT - Information on Result #1054521

Information on Result #1054521

Linear OOA(2¹¹⁰, 41, F₂, 4, 40) (dual of [(41, 4), 54, 41]-NRT-code), using OOA 2-folding based on linear OOA(2¹¹⁰, 82, F₂, 2, 40) (dual of [(82, 2), 54, 41]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹¹⁰, 83, F₂, 2, 40) (dual of [(83, 2), 56, 41]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2¹¹¹, 84, F₂, 2, 41) (dual of [(84, 2), 57, 42]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OOA(8²³, 21, F₈, 2, 20) (dual of [(21, 2), 19, 21]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(8²³, 24, F₈, 2, 20) (dual of [(24, 2), 25, 21]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,27P) [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.