MinT - Information on Result #1103871

Information on Result #1103871

Linear OOA(3¹²⁶, 42, F₃, 5, 51) (dual of [(42, 5), 84, 52]-NRT-code), using OOA 2-folding based on linear OOA(3¹²⁶, 84, F₃, 3, 51) (dual of [(84, 3), 126, 52]-NRT-code), using

trace code [i] based on linear OOA(9⁶³, 42, F₉, 3, 51) (dual of [(42, 3), 63, 52]-NRT-code), using
- constructionÂ X applied to AG(3;F,65P) âŠ‚ AG(3;F,70P) [i] based on
  1. linear OOA(9⁵⁹, 39, F₉, 3, 51) (dual of [(39, 3), 58, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,65P) [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]
  2. linear OOA(9⁵⁴, 39, F₉, 3, 46) (dual of [(39, 3), 63, 47]-NRT-code), using algebraic-geometric NRT-code AG(3;F,70P) [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40 (see above)
  3. linear OOA(9⁴, 3, F₉, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9⁴, 9, F₉, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;23,9) [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.