MinT - Information on Result #830044

Information on Result #830044

Linear OOA(4²²⁴, 231, F₄, 2, 69) (dual of [(231, 2), 238, 70]-NRT-code), using OOA 2-folding based on linear OA(4²²⁴, 462, F₄, 69) (dual of [462, 238, 70]-code), using

trace code [i] based on linear OA(16¹¹², 231, F₁₆, 69) (dual of [231, 119, 70]-code), using
- constructionÂ X applied to AG(F,154P) âŠ‚ AG(F,158P) [i] based on
  1. linear OA(16¹⁰⁹, 224, F₁₆, 69) (dual of [224, 115, 70]-code), using algebraic-geometric code AG(F,154P) [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 OA(16¹⁰⁵, 224, F₁₆, 65) (dual of [224, 119, 66]-code), using algebraic-geometric code AG(F,158P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OA(16³, 7, F₁₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
    - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
      - Reedâ€“Solomon code RS(13,16) [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.