MinT - Information on Result #967412

Information on Result #967412

Linear OOA(4²³⁸, 229, F₄, 3, 74) (dual of [(229, 3), 449, 75]-NRT-code), using OOA 2-folding based on linear OOA(4²³⁸, 458, F₄, 2, 74) (dual of [(458, 2), 678, 75]-NRT-code), using

trace code [i] based on linear OOA(16¹¹⁹, 229, F₁₆, 2, 74) (dual of [(229, 2), 339, 75]-NRT-code), using
- constructionÂ X applied to AG(2;F,373P) âŠ‚ AG(2;F,379P) [i] based on
  1. linear OOA(16¹¹⁴, 224, F₁₆, 2, 74) (dual of [(224, 2), 334, 75]-NRT-code), using algebraic-geometric NRT-code AG(2;F,373P) [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(16¹⁰⁸, 224, F₁₆, 2, 68) (dual of [(224, 2), 340, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,379P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OOA(16⁵, 5, F₁₆, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁵, 16, F₁₆, 2, 5) (dual of [(16, 2), 27, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;27,16) [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.