MinT - Information on Result #2704109

Information on Result #2704109

Linear OOA(9¹⁴⁹, 750, F₉, 3, 49) (dual of [(750, 3), 2101, 50]-NRT-code), using 9¹ times duplication based on linear OOA(9¹⁴⁸, 750, F₉, 3, 49) (dual of [(750, 3), 2102, 50]-NRT-code), using

trace code [i] based on linear OOA(81⁷⁴, 375, F₈₁, 3, 49) (dual of [(375, 3), 1051, 50]-NRT-code), using
- constructionÂ X applied to AG(3;F,1057P) âŠ‚ AG(3;F,1067P) [i] based on
  1. linear OOA(81⁶⁵, 369, F₈₁, 3, 49) (dual of [(369, 3), 1042, 50]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1057P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(81⁵⁵, 369, F₈₁, 3, 39) (dual of [(369, 3), 1052, 40]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1067P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁹, 6, F₈₁, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁹, 81, F₈₁, 3, 9) (dual of [(81, 3), 234, 10]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;234,81) [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.