MinT - Information on Result #1053143

Information on Result #1053143

Linear OOA(2⁵⁸, 19, F₂, 4, 27) (dual of [(19, 4), 18, 28]-NRT-code), using OOA 2-folding based on linear OOA(2⁵⁸, 38, F₂, 2, 27) (dual of [(38, 2), 18, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁵⁸, 39, F₂, 2, 27) (dual of [(39, 2), 20, 28]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4¹⁶, 13, F₄, 2, 13) (dual of [(13, 2), 10, 14]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹⁶, 14, F₄, 2, 13) (dual of [(14, 2), 12, 14]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,14P) [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.