MinT - Information on Result #1054337

Information on Result #1054337

Linear OOA(2¹¹⁰, 44, F₂, 4, 38) (dual of [(44, 4), 66, 39]-NRT-code), using OOA 2-folding based on linear OOA(2¹¹⁰, 88, F₂, 2, 38) (dual of [(88, 2), 66, 39]-NRT-code), using

strength reduction [i] based on linear OOA(2¹¹⁰, 88, F₂, 2, 39) (dual of [(88, 2), 66, 40]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(8²², 22, F₈, 2, 19) (dual of [(22, 2), 22, 20]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8²², 24, F₈, 2, 19) (dual of [(24, 2), 26, 20]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,28P) [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.