MinT - Information on Result #2634761

Information on Result #2634761

Linear OOA(4²⁰⁶, 77, F₄, 3, 138) (dual of [(77, 3), 25, 139]-NRT-code), using strength reduction based on linear OOA(4²⁰⁶, 77, F₄, 3, 139) (dual of [(77, 3), 25, 140]-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(4¹³¹, 52, F₄, 3, 98) (dual of [(52, 3), 25, 99]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹³¹, 55, F₄, 3, 98) (dual of [(55, 3), 34, 99]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,66P) [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.