MinT - Information on Result #1134473

Information on Result #1134473

Linear OOA(2¹⁰³, 20, F₂, 6, 56) (dual of [(20, 6), 17, 57]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁰³, 40, F₂, 3, 56) (dual of [(40, 3), 17, 57]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁰³, 41, F₂, 3, 56) (dual of [(41, 3), 20, 57]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2¹⁰⁴, 42, F₂, 3, 57) (dual of [(42, 3), 22, 58]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OOA(4³¹, 14, F₄, 3, 28) (dual of [(14, 3), 11, 29]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [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]

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.