MinT - Information on Result #1104677

Information on Result #1104677

Linear OOA(3²⁰⁶, 85, F₃, 5, 69) (dual of [(85, 5), 219, 70]-NRT-code), using OOA 2-folding based on linear OOA(3²⁰⁶, 170, F₃, 3, 69) (dual of [(170, 3), 304, 70]-NRT-code), using

trace code [i] based on linear OOA(9¹⁰³, 85, F₉, 3, 69) (dual of [(85, 3), 152, 70]-NRT-code), using
- constructionÂ X applied to AG(3;F,161P) âŠ‚ AG(3;F,174P) [i] based on
  1. linear OOA(9⁹¹, 77, F₉, 3, 69) (dual of [(77, 3), 140, 70]-NRT-code), using algebraic-geometric NRT-code AG(3;F,161P) [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(9⁷⁸, 77, F₉, 3, 56) (dual of [(77, 3), 153, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,174P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
  3. linear OOA(9¹², 8, F₉, 3, 12) (dual of [(8, 3), 12, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9¹², 9, F₉, 3, 12) (dual of [(9, 3), 15, 13]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;15,9) [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.