MinT - Information on Result #986537

Information on Result #986537

Linear OOA(9¹¹⁰, 176, F₉, 3, 43) (dual of [(176, 3), 418, 44]-NRT-code), using OOA 2-folding based on linear OOA(9¹¹⁰, 352, F₉, 2, 43) (dual of [(352, 2), 594, 44]-NRT-code), using

trace code [i] based on linear OOA(81⁵⁵, 176, F₈₁, 2, 43) (dual of [(176, 2), 297, 44]-NRT-code), using
- constructionÂ X applied to AG(2;F,298P) âŠ‚ AG(2;F,304P) [i] based on
  1. linear OOA(81⁵⁰, 171, F₈₁, 2, 43) (dual of [(171, 2), 292, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,298P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]
  2. linear OOA(81⁴⁴, 171, F₈₁, 2, 37) (dual of [(171, 2), 298, 38]-NRT-code), using algebraic-geometric NRT-code AG(2;F,304P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172 (see above)
  3. linear OOA(81⁵, 5, F₈₁, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁵, 81, F₈₁, 2, 5) (dual of [(81, 2), 157, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;157,81) [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.