MinT - Information on Result #945652

Information on Result #945652

Linear OOA(2⁴¹, 18, F₂, 3, 17) (dual of [(18, 3), 13, 18]-NRT-code), using OOA 3-folding based on linear OA(2⁴¹, 54, F₂, 17) (dual of [54, 13, 18]-code), using

discarding factors / shortening the dual code based on linear OA(2⁴¹, 56, F₂, 17) (dual of [56, 15, 18]-code), using
- concatenation of two codes [i] based on
  1. linear OA(8⁹, 14, F₈, 8) (dual of [14, 5, 9]-code), using
    - extended algebraic-geometric code AG_e(F,5P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
  2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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.