MinT - Information on Result #669129

Information on Result #669129

Linear OA(49⁵³, 110, F₄₉, 33) (dual of [110, 57, 34]-code), using (u,Â u+v)-construction based on

linear OA(49¹⁸, 55, F₄₉, 16) (dual of [55, 37, 17]-code), using
- constructionÂ X applied to AG(F,11P) âŠ‚ AG(F,12P) [i] based on
  1. linear OA(49¹⁶, 50, F₄₉, 16) (dual of [50, 34, 17]-code or 50-arc in PG(15,49)), using algebraic-geometric code AG(F, Q+15P) with degQ = 3 and 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(49¹³, 50, F₄₉, 13) (dual of [50, 37, 14]-code or 50-arc in PG(12,49)), using algebraic-geometric code AG(F,18P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  3. linear OA(49², 5, F₄₉, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,49)), using
    - discarding factors / shortening the dual code based on linear OA(49², 49, F₄₉, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
      - Reedâ€“Solomon code RS(47,49) [i]
linear OA(49³⁵, 55, F₄₉, 33) (dual of [55, 20, 34]-code), using
- constructionÂ X applied to AG(F, Q+4P) âŠ‚ AG(F, Q+5P) [i] based on
  1. linear OA(49³³, 50, F₄₉, 33) (dual of [50, 17, 34]-code or 50-arc in PG(32,49)), using algebraic-geometric code AG(F,8P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  2. linear OA(49³⁰, 50, F₄₉, 30) (dual of [50, 20, 31]-code or 50-arc in PG(29,49)), using algebraic-geometric code AG(F, Q+8P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  3. linear OA(49², 5, F₄₉, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,49)) (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.