MinT - Information on Result #1099658

Information on Result #1099658

Linear OOA(2¹⁷⁸, 39, F₂, 5, 80) (dual of [(39, 5), 17, 81]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁷⁸, 78, F₂, 3, 80) (dual of [(78, 3), 56, 81]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁷⁸, 78, F₂, 3, 81) (dual of [(78, 3), 56, 82]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4⁵⁰, 26, F₄, 3, 40) (dual of [(26, 3), 28, 41]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,37P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, 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.