MinT - Information on Result #2670228

Information on Result #2670228

Linear OOA(2¹²², 57, F₂, 3, 50) (dual of [(57, 3), 49, 51]-NRT-code), using 2¹ times duplication based on linear OOA(2¹²¹, 57, F₂, 3, 50) (dual of [(57, 3), 50, 51]-NRT-code), using

strength reduction [i] based on linear OOA(2¹²¹, 57, F₂, 3, 51) (dual of [(57, 3), 50, 52]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4³², 19, F₄, 3, 25) (dual of [(19, 3), 25, 26]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4³², 21, F₄, 3, 25) (dual of [(21, 3), 31, 26]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,37P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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.