MinT - Information on Result #986847

Information on Result #986847

Linear OOA(9¹⁵⁰, 378, F₉, 3, 50) (dual of [(378, 3), 984, 51]-NRT-code), using OOA 2-folding based on linear OOA(9¹⁵⁰, 756, F₉, 2, 50) (dual of [(756, 2), 1362, 51]-NRT-code), using

trace code [i] based on linear OOA(81⁷⁵, 378, F₈₁, 2, 50) (dual of [(378, 2), 681, 51]-NRT-code), using
- constructionÂ X applied to AG(2;F,687P) âŠ‚ AG(2;F,697P) [i] based on
  1. linear OOA(81⁶⁶, 369, F₈₁, 2, 50) (dual of [(369, 2), 672, 51]-NRT-code), using algebraic-geometric NRT-code AG(2;F,687P) [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(81⁵⁶, 369, F₈₁, 2, 40) (dual of [(369, 2), 682, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,697P) [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.