MinT - Information on Result #1052331

Information on Result #1052331

Linear OOA(2³⁸, 12, F₂, 4, 20) (dual of [(12, 4), 10, 21]-NRT-code), using OOA 2-folding based on linear OOA(2³⁸, 24, F₂, 2, 20) (dual of [(24, 2), 10, 21]-NRT-code), using

strength reduction [i] based on linear OOA(2³⁸, 24, F₂, 2, 21) (dual of [(24, 2), 10, 22]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4¹¹, 8, F₄, 2, 10) (dual of [(8, 2), 5, 11]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹¹, 9, F₄, 2, 10) (dual of [(9, 2), 7, 11]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [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.