MinT - Information on Result #2663429

Information on Result #2663429

Linear OOA(4²¹⁹, 79, F₄, 3, 160) (dual of [(79, 3), 18, 161]-NRT-code), using 3 step truncation based on linear OOA(4²²², 80, F₄, 3, 163) (dual of [(80, 3), 18, 164]-NRT-code), using

constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,50P) [i] based on
1. linear OOA(4¹⁶⁴, 55, F₄, 3, 164) (dual of [(55, 3), 1, 165]-NRT-code), using algebraic-geometric NRT-code AG(3;F,0P) [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]
2. linear OOA(4¹⁴⁷, 55, F₄, 3, 114) (dual of [(55, 3), 18, 115]-NRT-code), using algebraic-geometric NRT-code AG(3;F,50P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁵⁸, 25, F₄, 3, 48) (dual of [(25, 3), 17, 49]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁵⁸, 26, F₄, 3, 48) (dual of [(26, 3), 20, 49]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,29P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [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.