MinT - Information on Result #860997

Information on Result #860997

Linear OOA(25⁵⁶, 195330, F₂₅, 2, 13) (dual of [(195330, 2), 390604, 14]-NRT-code), using OOA 2-folding based on linear OA(25⁵⁶, 390660, F₂₅, 13) (dual of [390660, 390604, 14]-code), using

discarding factors / shortening the dual code based on linear OA(25⁵⁶, 390661, F₂₅, 13) (dual of [390661, 390605, 14]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(25⁶, 26, F₂₅, 6) (dual of [26, 20, 7]-code or 26-arc in PG(5,25)), using
    - extended Reedâ€“Solomon code RS_e(20,25) [i]
    - 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]
    - algebraic-geometric code AG(F, Q+5P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
  2. linear OA(25⁵⁰, 390635, F₂₅, 13) (dual of [390635, 390585, 14]-code), using
    - constructionÂ X applied to C([0,6]) âŠ‚ C([0,5]) [i] based on
      1. 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]
      2. linear OA(25⁴¹, 390626, F₂₅, 11) (dual of [390626, 390585, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
      3. linear OA(25¹, 9, F₂₅, 1) (dual of [9, 8, 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]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.