MinT - Information on Result #859851

Information on Result #859851

Linear OOA(16¹¹⁴, 116, F₁₆, 2, 70) (dual of [(116, 2), 118, 71]-NRT-code), using OOA 2-folding based on linear OA(16¹¹⁴, 232, F₁₆, 70) (dual of [232, 118, 71]-code), using

discarding factors / shortening the dual code based on linear OA(16¹¹⁴, 233, F₁₆, 70) (dual of [233, 119, 71]-code), using
- constructionÂ X applied to AG(F,153P) âŠ‚ AG(F,158P) [i] based on
  1. linear OA(16¹¹⁰, 224, F₁₆, 70) (dual of [224, 114, 71]-code), using algebraic-geometric code AG(F,153P) [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(16⁴, 9, F₁₆, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,16)), using
    - discarding factors / shortening the dual code based on linear OA(16⁴, 16, F₁₆, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
      - Reedâ€“Solomon code RS(12,16) [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.