MinT - Information on Result #2636179

Information on Result #2636179

Linear OOA(4²²⁵, 81, F₄, 3, 164) (dual of [(81, 3), 18, 165]-NRT-code), using strength reduction based on linear OOA(4²²⁵, 81, F₄, 3, 165) (dual of [(81, 3), 18, 166]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁵⁷, 25, F₄, 3, 47) (dual of [(25, 3), 18, 48]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁵⁷, 26, F₄, 3, 47) (dual of [(26, 3), 21, 48]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,30P) [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(4¹⁵⁰, 56, F₄, 3, 117) (dual of [(56, 3), 18, 118]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,50P) [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.