MinT - Information on Result #986808

Information on Result #986808

Linear OOA(9¹⁴⁸, 378, F₉, 3, 49) (dual of [(378, 3), 986, 50]-NRT-code), using OOA 2-folding based on linear OOA(9¹⁴⁸, 756, F₉, 2, 49) (dual of [(756, 2), 1364, 50]-NRT-code), using

trace code [i] based on linear OOA(81⁷⁴, 378, F₈₁, 2, 49) (dual of [(378, 2), 682, 50]-NRT-code), using
- constructionÂ X applied to AG(2;F,688P) âŠ‚ AG(2;F,698P) [i] based on
  1. linear OOA(81⁶⁵, 369, F₈₁, 2, 49) (dual of [(369, 2), 673, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,688P) [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, 2, 39) (dual of [(369, 2), 683, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,698P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁹, 9, F₈₁, 2, 9) (dual of [(9, 2), 9, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁹, 81, F₈₁, 2, 9) (dual of [(81, 2), 153, 10]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;153,81) [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.