MinT - Information on Result #2514078

Information on Result #2514078

Linear OOA(9¹³³, 748, F₉, 2, 45) (dual of [(748, 2), 1363, 46]-NRT-code), using 9¹ times duplication based on linear OOA(9¹³², 748, F₉, 2, 45) (dual of [(748, 2), 1364, 46]-NRT-code), using

trace code [i] based on linear OOA(81⁶⁶, 374, F₈₁, 2, 45) (dual of [(374, 2), 682, 46]-NRT-code), using
- constructionÂ X applied to AG(2;F,692P) âŠ‚ AG(2;F,698P) [i] based on
  1. linear OOA(81⁶¹, 369, F₈₁, 2, 45) (dual of [(369, 2), 677, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,692P) [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(81⁵⁵, 369, F₈₁, 2, 39) (dual of [(369, 2), 683, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,698P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (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.