MinT - Information on Result #1103654

Information on Result #1103654

Linear OOA(3¹⁵⁰, 81, F₃, 5, 47) (dual of [(81, 5), 255, 48]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁵⁰, 162, F₃, 3, 47) (dual of [(162, 3), 336, 48]-NRT-code), using

trace code [i] based on linear OOA(9⁷⁵, 81, F₉, 3, 47) (dual of [(81, 3), 168, 48]-NRT-code), using
- constructionÂ X applied to AG(3;F,183P) âŠ‚ AG(3;F,190P) [i] based on
  1. linear OOA(9⁶⁹, 77, F₉, 3, 47) (dual of [(77, 3), 162, 48]-NRT-code), using algebraic-geometric NRT-code AG(3;F,183P) [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(9⁶², 77, F₉, 3, 40) (dual of [(77, 3), 169, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,190P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
  3. linear OOA(9⁶, 4, F₉, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9⁶, 9, F₉, 3, 6) (dual of [(9, 3), 21, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;21,9) [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.