MinT - Information on Result #860162

Information on Result #860162

Linear OOA(16¹²⁸, 123, F₁₆, 2, 78) (dual of [(123, 2), 118, 79]-NRT-code), using OOA 2-folding based on linear OA(16¹²⁸, 246, F₁₆, 78) (dual of [246, 118, 79]-code), using

discarding factors / shortening the dual code based on linear OA(16¹²⁸, 247, F₁₆, 78) (dual of [247, 119, 79]-code), using
- constructionÂ X applied to AG(F,163P) âŠ‚ AG(F,166P) [i] based on
  1. linear OA(16¹²⁶, 242, F₁₆, 78) (dual of [242, 116, 79]-code), using algebraic-geometric code AG(F,163P) [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(16¹²³, 242, F₁₆, 75) (dual of [242, 119, 76]-code), using algebraic-geometric code AG(F,166P) [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243 (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.