MinT - Information on Result #2634998

Information on Result #2634998

Linear OOA(4²⁰⁹, 78, F₄, 3, 141) (dual of [(78, 3), 25, 142]-NRT-code), using strength reduction based on linear OOA(4²⁰⁹, 78, F₄, 3, 142) (dual of [(78, 3), 25, 143]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁵⁰, 25, F₄, 3, 40) (dual of [(25, 3), 25, 41]-NRT-code), using
  - discarding factors / shortening the dual code based on 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 OOA(4¹³⁴, 53, F₄, 3, 101) (dual of [(53, 3), 25, 102]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹³⁴, 55, F₄, 3, 101) (dual of [(55, 3), 31, 102]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,63P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [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.