MinT - Information on Result #669324

Information on Result #669324

Linear OA(49³⁸, 5764855, F₄₉, 9) (dual of [5764855, 5764817, 10]-code), using (u,Â u+v)-construction based on

linear OA(49⁵, 53, F₄₉, 4) (dual of [53, 48, 5]-code), using
- constructionÂ X applied to AG(F, Q+21P) âŠ‚ AG(F, Q+22P) [i] based on
  1. linear OA(49⁴, 50, F₄₉, 4) (dual of [50, 46, 5]-code or 50-arc in PG(3,49)), using algebraic-geometric code AG(F, Q+21P) 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(49², 50, F₄₉, 2) (dual of [50, 48, 3]-code or 50-arc in PG(1,49)), using algebraic-geometric code AG(F, Q+22P) 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(49³³, 5764802, F₄₉, 9) (dual of [5764802, 5764769, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

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