MinT - Information on Result #669144

Information on Result #669144

Linear OA(49⁴⁴, 103, F₄₉, 29) (dual of [103, 59, 30]-code), using (u,Â u+v)-construction based on

linear OA(49¹⁴, 50, F₄₉, 14) (dual of [50, 36, 15]-code or 50-arc in PG(13,49)), using
- extended Reedâ€“Solomon code RS_e(36,49) [i]
- algebraic-geometric code AG(F, Q+16P) 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, Q+11P) with degQ = 2 and 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,7P) with degPÂ =Â 5 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
linear OA(49³⁰, 53, F₄₉, 29) (dual of [53, 23, 30]-code), using
- constructionÂ X applied to AG(F,10P) âŠ‚ AG(F,11P) [i] based on
  1. linear OA(49²⁹, 50, F₄₉, 29) (dual of [50, 21, 30]-code or 50-arc in PG(28,49)), using algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  2. linear OA(49²⁷, 50, F₄₉, 27) (dual of [50, 23, 28]-code or 50-arc in PG(26,49)), using algebraic-geometric code AG(F,11P) 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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