MinT - Information on Result #2707370

Information on Result #2707370

OOA(64⁶⁹, 290, S₆₄, 3, 45), using strength reduction based on OOA(64⁶⁹, 290, S₆₄, 3, 46), using

discarding parts of the base [i] based on linear OOA(128⁵⁹, 290, F₁₂₈, 3, 46) (dual of [(290, 3), 811, 47]-NRT-code), using
- constructionÂ X applied to AG(3;F,814P) âŠ‚ AG(3;F,819P) [i] based on
  1. linear OOA(128⁵⁵, 287, F₁₂₈, 3, 46) (dual of [(287, 3), 806, 47]-NRT-code), using algebraic-geometric NRT-code AG(3;F,814P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]
  2. linear OOA(128⁵⁰, 287, F₁₂₈, 3, 41) (dual of [(287, 3), 811, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,819P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
  3. linear OOA(128⁴, 3, F₁₂₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁴, 128, F₁₂₈, 3, 4) (dual of [(128, 3), 380, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;380,128) [i]

Mode: Constructive.

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.