MinT - Information on Result #2682732

Information on Result #2682732

Linear OOA(3²²⁵, 166, F₃, 3, 81) (dual of [(166, 3), 273, 82]-NRT-code), using 3¹ times duplication based on linear OOA(3²²⁴, 166, F₃, 3, 81) (dual of [(166, 3), 274, 82]-NRT-code), using

trace code [i] based on linear OOA(9¹¹², 83, F₉, 3, 81) (dual of [(83, 3), 137, 82]-NRT-code), using
- constructionÂ X applied to AG(3;F,149P) âŠ‚ AG(3;F,159P) [i] based on
  1. linear OOA(9¹⁰³, 77, F₉, 3, 81) (dual of [(77, 3), 128, 82]-NRT-code), using algebraic-geometric NRT-code AG(3;F,149P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]
  2. linear OOA(9⁹³, 77, F₉, 3, 71) (dual of [(77, 3), 138, 72]-NRT-code), using algebraic-geometric NRT-code AG(3;F,159P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
  3. linear OOA(9⁹, 6, F₉, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9⁹, 9, F₉, 3, 9) (dual of [(9, 3), 18, 10]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;18,9) [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.