MinT - Information on Result #2277985

Information on Result #2277985

Linear OA(5¹²³, 261, F₅, 49) (dual of [261, 138, 50]-code), using 1 times code embedding in larger space based on linear OA(5¹²², 260, F₅, 49) (dual of [260, 138, 50]-code), using

trace code [i] based on linear OA(25⁶¹, 130, F₂₅, 49) (dual of [130, 69, 50]-code), using
- constructionÂ X applied to AG(F,75P) âŠ‚ AG(F,78P) [i] based on
  1. linear OA(25⁵⁹, 125, F₂₅, 49) (dual of [125, 66, 50]-code), using algebraic-geometric code AG(F,75P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]
  2. linear OA(25⁵⁶, 125, F₂₅, 46) (dual of [125, 69, 47]-code), using algebraic-geometric code AG(F,78P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (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.