MinT - Information on Result #1055628

Information on Result #1055628

Linear OOA(2¹²⁹, 42, F₂, 4, 52) (dual of [(42, 4), 39, 53]-NRT-code), using OOA 2-folding based on linear OOA(2¹²⁹, 84, F₂, 2, 52) (dual of [(84, 2), 39, 53]-NRT-code), using

strength reduction [i] based on linear OOA(2¹²⁹, 84, F₂, 2, 53) (dual of [(84, 2), 39, 54]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(8²⁹, 21, F₈, 2, 26) (dual of [(21, 2), 13, 27]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8²⁹, 24, F₈, 2, 26) (dual of [(24, 2), 19, 27]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,21P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
        the Klein quartic over F₈ [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.