MinT - Information on Result #2663537

Information on Result #2663537

Linear OOA(4²¹², 81, F₄, 3, 140) (dual of [(81, 3), 31, 141]-NRT-code), using 3 step truncation based on linear OOA(4²¹⁵, 82, F₄, 3, 143) (dual of [(82, 3), 31, 144]-NRT-code), using

constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,63P) [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(4¹³⁴, 55, F₄, 3, 101) (dual of [(55, 3), 31, 102]-NRT-code), using algebraic-geometric NRT-code AG(3;F,63P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁵¹, 27, F₄, 3, 41) (dual of [(27, 3), 30, 42]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,39P) [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.