MinT - Information on Result #3176851

Information on Result #3176851

Digital (65, 85, 39065)-net over F₂₅, using 1 times m-reduction based on digital (65, 86, 39065)-net over F₂₅, using

net defined by OOA [i] based on linear OOA(25⁸⁶, 39065, F₂₅, 21, 21) (dual of [(39065, 21), 820279, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25⁸⁶, 390651, F₂₅, 21) (dual of [390651, 390565, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁸⁶, 390652, F₂₅, 21) (dual of [390652, 390566, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(25⁸¹, 390626, F₂₅, 21) (dual of [390626, 390545, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(25⁵⁷, 390626, F₂₅, 15) (dual of [390626, 390569, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      3. linear OA(25⁵, 26, F₂₅, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
        extended Reedâ€“Solomon code RS_e(21,25) [i]
        the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        algebraic-geometric code AG(F,10P) with 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+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.