MinT - Information on Result #836921

Information on Result #836921

Linear OOA(5⁶⁴, 70, F₅, 2, 26) (dual of [(70, 2), 76, 27]-NRT-code), using OOA 2-folding based on linear OA(5⁶⁴, 140, F₅, 26) (dual of [140, 76, 27]-code), using

trace code [i] based on linear OA(25³², 70, F₂₅, 26) (dual of [70, 38, 27]-code), using
- constructionÂ X applied to AG(F,38P) âŠ‚ AG(F,41P) [i] based on
  1. linear OA(25³⁰, 65, F₂₅, 26) (dual of [65, 35, 27]-code), using algebraic-geometric code AG(F,38P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(25²⁷, 65, F₂₅, 23) (dual of [65, 38, 24]-code), using algebraic-geometric code AG(F,41P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
  3. linear OA(25², 5, F₂₅, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
    - discarding factors / shortening the dual code based on linear OA(25², 25, F₂₅, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
      - Reedâ€“Solomon code RS(23,25) [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.