MinT - Information on Result #2278046

Information on Result #2278046

Linear OA(5¹³³, 269, F₅, 52) (dual of [269, 136, 53]-code), using 1 times code embedding in larger space based on linear OA(5¹³², 268, F₅, 52) (dual of [268, 136, 53]-code), using

trace code [i] based on linear OA(25⁶⁶, 134, F₂₅, 52) (dual of [134, 68, 53]-code), using
- constructionÂ X applied to AG(F,72P) âŠ‚ AG(F,77P) [i] based on
  1. linear OA(25⁶², 125, F₂₅, 52) (dual of [125, 63, 53]-code), using algebraic-geometric code AG(F,72P) [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(25⁵⁷, 125, F₂₅, 47) (dual of [125, 68, 48]-code), using algebraic-geometric code AG(F,77P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126 (see above)
  3. linear OA(25⁴, 9, F₂₅, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,25)), using
    - discarding factors / shortening the dual code based on linear OA(25⁴, 25, F₂₅, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
      - Reedâ€“Solomon code RS(21,25) [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.