MinT - Information on Result #2703847

Information on Result #2703847

Linear OOA(9¹²⁷, 745, F₉, 3, 42) (dual of [(745, 3), 2108, 43]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(9¹²⁴, 744, F₉, 3, 42) (dual of [(744, 3), 2108, 43]-NRT-code), using

trace code [i] based on linear OOA(81⁶², 372, F₈₁, 3, 42) (dual of [(372, 3), 1054, 43]-NRT-code), using
- constructionÂ X applied to AG(3;F,1064P) âŠ‚ AG(3;F,1069P) [i] based on
  1. linear OOA(81⁵⁸, 369, F₈₁, 3, 42) (dual of [(369, 3), 1049, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1064P) [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(81⁵³, 369, F₈₁, 3, 37) (dual of [(369, 3), 1054, 38]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1069P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁴, 3, F₈₁, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁴, 81, F₈₁, 3, 4) (dual of [(81, 3), 239, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;239,81) [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.