MinT - Information on Result #669164

Information on Result #669164

Linear OA(49⁴⁰, 108, F₄₉, 25) (dual of [108, 68, 26]-code), using (u,Â u+v)-construction based on

linear OA(49¹³, 53, F₄₉, 12) (dual of [53, 40, 13]-code), using
- constructionÂ X applied to AG(F, Q+17P) âŠ‚ AG(F, Q+18P) [i] based on
  1. linear OA(49¹², 50, F₄₉, 12) (dual of [50, 38, 13]-code or 50-arc in PG(11,49)), using algebraic-geometric code AG(F, Q+17P) 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(49¹⁰, 50, F₄₉, 10) (dual of [50, 40, 11]-code or 50-arc in PG(9,49)), using algebraic-geometric code AG(F, Q+18P) 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(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(49²⁷, 55, F₄₉, 25) (dual of [55, 28, 26]-code), using
- constructionÂ X applied to AG(F,8P) âŠ‚ AG(F,9P) [i] based on
  1. linear OA(49²⁵, 50, F₄₉, 25) (dual of [50, 25, 26]-code or 50-arc in PG(24,49)), using algebraic-geometric code AG(F,12P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  2. linear OA(49²², 50, F₄₉, 22) (dual of [50, 28, 23]-code or 50-arc in PG(21,49)), using algebraic-geometric code AG(F, Q+12P) 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)), 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]

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.