MinT - Information on Result #669171

Information on Result #669171

Linear OA(49³⁶, 106, F₄₉, 23) (dual of [106, 70, 24]-code), using (u,Â u+v)-construction based on

linear OA(49¹², 53, F₄₉, 11) (dual of [53, 41, 12]-code), using
- constructionÂ X applied to AG(F,19P) âŠ‚ AG(F,20P) [i] based on
  1. linear OA(49¹¹, 50, F₄₉, 11) (dual of [50, 39, 12]-code or 50-arc in PG(10,49)), using algebraic-geometric code AG(F,19P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using the rational function field F₄₉(x) [i]
  2. linear OA(49⁹, 50, F₄₉, 9) (dual of [50, 41, 10]-code or 50-arc in PG(8,49)), using algebraic-geometric code AG(F,20P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  3. linear OA(49¹, 3, F₄₉, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(49²⁴, 53, F₄₉, 23) (dual of [53, 29, 24]-code), using
- constructionÂ X applied to AG(F,13P) âŠ‚ AG(F,14P) [i] based on
  1. linear OA(49²³, 50, F₄₉, 23) (dual of [50, 27, 24]-code or 50-arc in PG(22,49)), using algebraic-geometric code AG(F,13P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  2. linear OA(49²¹, 50, F₄₉, 21) (dual of [50, 29, 22]-code or 50-arc in PG(20,49)), using algebraic-geometric code AG(F,14P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  3. linear OA(49¹, 3, F₄₉, 1) (dual of [3, 2, 2]-code) (see above)

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.