MinT - Information on Result #2703485

Information on Result #2703485

Linear OOA(9¹¹³, 748, F₉, 3, 33) (dual of [(748, 3), 2131, 34]-NRT-code), using 9¹ times duplication based on linear OOA(9¹¹², 748, F₉, 3, 33) (dual of [(748, 3), 2132, 34]-NRT-code), using

trace code [i] based on linear OOA(81⁵⁶, 374, F₈₁, 3, 33) (dual of [(374, 3), 1066, 34]-NRT-code), using
- constructionÂ X applied to AG(3;F,1073P) âŠ‚ AG(3;F,1081P) [i] based on
  1. linear OOA(81⁴⁹, 369, F₈₁, 3, 33) (dual of [(369, 3), 1058, 34]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1073P) [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(81⁴¹, 369, F₈₁, 3, 25) (dual of [(369, 3), 1066, 26]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1081P) [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.