MinT - Information on Result #2487345

Information on Result #2487345

Linear OOA(3⁸³, 84, F₃, 2, 30) (dual of [(84, 2), 85, 31]-NRT-code), using 3¹ times duplication based on linear OOA(3⁸², 84, F₃, 2, 30) (dual of [(84, 2), 86, 31]-NRT-code), using

trace code [i] based on linear OOA(9⁴¹, 42, F₉, 2, 30) (dual of [(42, 2), 43, 31]-NRT-code), using
- constructionÂ X applied to AG(2;F,47P) âŠ‚ AG(2;F,51P) [i] based on
  1. linear OOA(9³⁸, 39, F₉, 2, 30) (dual of [(39, 2), 40, 31]-NRT-code), using algebraic-geometric NRT-code AG(2;F,47P) [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(9³⁴, 39, F₉, 2, 26) (dual of [(39, 2), 44, 27]-NRT-code), using algebraic-geometric NRT-code AG(2;F,51P) [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40 (see above)
  3. linear OOA(9³, 3, F₉, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9³, 9, F₉, 2, 3) (dual of [(9, 2), 15, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;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.