MinT - Information on Result #859717

Information on Result #859717

Linear OOA(16¹⁰⁹, 114, F₁₆, 2, 67) (dual of [(114, 2), 119, 68]-NRT-code), using OOA 2-folding based on linear OA(16¹⁰⁹, 228, F₁₆, 67) (dual of [228, 119, 68]-code), using

discarding factors / shortening the dual code based on linear OA(16¹⁰⁹, 229, F₁₆, 67) (dual of [229, 120, 68]-code), using
- constructionÂ X applied to AG(F,156P) âŠ‚ AG(F,159P) [i] based on
  1. linear OA(16¹⁰⁷, 224, F₁₆, 67) (dual of [224, 117, 68]-code), using algebraic-geometric code AG(F,156P) [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(16¹⁰⁴, 224, F₁₆, 64) (dual of [224, 120, 65]-code), using algebraic-geometric code AG(F,159P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OA(16², 5, F₁₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
    - discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
      - Reedâ€“Solomon code RS(14,16) [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.