MinT - Information on Result #669126

Information on Result #669126

Linear OA(49⁵⁰, 103, F₄₉, 33) (dual of [103, 53, 34]-code), using (u,Â u+v)-construction based on

linear OA(49¹⁶, 50, F₄₉, 16) (dual of [50, 34, 17]-code or 50-arc in PG(15,49)), using
- extended Reedâ€“Solomon code RS_e(34,49) [i]
- 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]
- algebraic-geometric code AG(F,11P) with degPÂ =Â 3 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
- algebraic-geometric code AG(F, Q+6P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
linear OA(49³⁴, 53, F₄₉, 33) (dual of [53, 19, 34]-code), using
- constructionÂ X applied to AG(F,8P) âŠ‚ AG(F,9P) [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(49³¹, 50, F₄₉, 31) (dual of [50, 19, 32]-code or 50-arc in PG(30,49)), using algebraic-geometric code AG(F,9P) 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.

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