MinT - Information on Result #2279185

Information on Result #2279185

Linear OA(7⁴⁵, 107, F₇, 21) (dual of [107, 62, 22]-code), using 1 times code embedding in larger space based on linear OA(7⁴⁴, 106, F₇, 21) (dual of [106, 62, 22]-code), using

trace code [i] based on linear OA(49²², 53, F₄₉, 21) (dual of [53, 31, 22]-code), using
- constructionÂ X applied to AG(F,14P) âŠ‚ AG(F,15P) [i] based on
  1. 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, using the rational function field F₄₉(x) [i]
  2. linear OA(49¹⁹, 50, F₄₉, 19) (dual of [50, 31, 20]-code or 50-arc in PG(18,49)), using algebraic-geometric code AG(F,15P) 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]

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.