MinT - Information on Result #666333

Information on Result #666333

Linear OA(25⁷⁴, 390655, F₂₅, 17) (dual of [390655, 390581, 18]-code), using (u,Â u+v)-construction based on

linear OA(25⁹, 29, F₂₅, 8) (dual of [29, 20, 9]-code), using
- constructionÂ X applied to AG(F, Q+7P) âŠ‚ AG(F, Q+8P) [i] based on
  1. linear OA(25⁸, 26, F₂₅, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using algebraic-geometric code AG(F, Q+7P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
  2. linear OA(25⁶, 26, F₂₅, 6) (dual of [26, 20, 7]-code or 26-arc in PG(5,25)), using algebraic-geometric code AG(F, Q+8P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
  3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(25⁶⁵, 390626, F₂₅, 17) (dual of [390626, 390561, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and linear.

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