MinT - Information on Result #2635507

Information on Result #2635507

Linear OOA(4²¹⁶, 81, F₄, 3, 146) (dual of [(81, 3), 27, 147]-NRT-code), using strength reduction based on linear OOA(4²¹⁶, 81, F₄, 3, 147) (dual of [(81, 3), 27, 148]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁵⁴, 27, F₄, 3, 44) (dual of [(27, 3), 27, 45]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,36P) [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(4¹³⁵, 54, F₄, 3, 102) (dual of [(54, 3), 27, 103]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹³⁵, 55, F₄, 3, 102) (dual of [(55, 3), 30, 103]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,62P) [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.