MinT - Information on Result #666404

Information on Result #666404

Linear OA(25⁵⁶, 390655, F₂₅, 13) (dual of [390655, 390599, 14]-code), using (u,Â u+v)-construction based on

linear OA(25⁷, 29, F₂₅, 6) (dual of [29, 22, 7]-code), using
- constructionÂ X applied to AG(F, Q+8P) âŠ‚ AG(F, Q+9P) [i] based on
  1. 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, using the rational function field F₂₅(x) [i]
  2. linear OA(25⁴, 26, F₂₅, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using algebraic-geometric code AG(F, Q+9P) 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(25⁴⁹, 390626, F₂₅, 13) (dual of [390626, 390577, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

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