MinT - Information on Result #860127

Information on Result #860127

Linear OOA(16¹²⁸, 124, F₁₆, 2, 77) (dual of [(124, 2), 120, 78]-NRT-code), using OOA 2-folding based on linear OA(16¹²⁸, 248, F₁₆, 77) (dual of [248, 120, 78]-code), using

discarding factors / shortening the dual code based on linear OA(16¹²⁸, 249, F₁₆, 77) (dual of [249, 121, 78]-code), using
- constructionÂ X applied to AG(F,164P) âŠ‚ AG(F,168P) [i] based on
  1. linear OA(16¹²⁵, 242, F₁₆, 77) (dual of [242, 117, 78]-code), using algebraic-geometric code AG(F,164P) [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(16¹²¹, 242, F₁₆, 73) (dual of [242, 121, 74]-code), using algebraic-geometric code AG(F,168P) [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243 (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.