MinT - Information on Result #2703773

Information on Result #2703773

Linear OOA(9¹²⁹, 749, F₉, 3, 40) (dual of [(749, 3), 2118, 41]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(9¹²⁶, 748, F₉, 3, 40) (dual of [(748, 3), 2118, 41]-NRT-code), using

trace code [i] based on linear OOA(81⁶³, 374, F₈₁, 3, 40) (dual of [(374, 3), 1059, 41]-NRT-code), using
- constructionÂ X applied to AG(3;F,1066P) âŠ‚ AG(3;F,1074P) [i] based on
  1. linear OOA(81⁵⁶, 369, F₈₁, 3, 40) (dual of [(369, 3), 1051, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1066P) [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(81⁴⁸, 369, F₈₁, 3, 32) (dual of [(369, 3), 1059, 33]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1074P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁷, 5, F₈₁, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁷, 81, F₈₁, 3, 7) (dual of [(81, 3), 236, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;236,81) [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.