MinT - Information on Result #967496

Information on Result #967496

Linear OOA(4²⁴⁴, 231, F₄, 3, 75) (dual of [(231, 3), 449, 76]-NRT-code), using OOA 2-folding based on linear OOA(4²⁴⁴, 462, F₄, 2, 75) (dual of [(462, 2), 680, 76]-NRT-code), using

trace code [i] based on linear OOA(16¹²², 231, F₁₆, 2, 75) (dual of [(231, 2), 340, 76]-NRT-code), using
- constructionÂ X applied to AG(2;F,372P) âŠ‚ AG(2;F,380P) [i] based on
  1. linear OOA(16¹¹⁵, 224, F₁₆, 2, 75) (dual of [(224, 2), 333, 76]-NRT-code), using algebraic-geometric NRT-code AG(2;F,372P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(16¹⁰⁷, 224, F₁₆, 2, 67) (dual of [(224, 2), 341, 68]-NRT-code), using algebraic-geometric NRT-code AG(2;F,380P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OOA(16⁷, 7, F₁₆, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁷, 16, F₁₆, 2, 7) (dual of [(16, 2), 25, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;25,16) [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.