MinT - Information on Result #2634306

Information on Result #2634306

Linear OOA(4¹⁹⁹, 73, F₄, 3, 139) (dual of [(73, 3), 20, 140]-NRT-code), using strength reduction based on linear OOA(4¹⁹⁹, 73, F₄, 3, 140) (dual of [(73, 3), 20, 141]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁴⁰, 20, F₄, 3, 33) (dual of [(20, 3), 20, 34]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁴⁰, 21, F₄, 3, 33) (dual of [(21, 3), 23, 34]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,29P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]
2. linear OOA(4¹³⁹, 53, F₄, 3, 106) (dual of [(53, 3), 20, 107]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹³⁹, 55, F₄, 3, 106) (dual of [(55, 3), 26, 107]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,58P) [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.