MinT - Information on Result #1196296

Information on Result #1196296

Digital (43, 56, 65114)-net over F₂₅, using net defined by OOA based on linear OOA(25⁵⁶, 65114, F₂₅, 14, 13) (dual of [(65114, 14), 911540, 14]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(25⁵⁶, 195343, F₂₅, 2, 13) (dual of [(195343, 2), 390630, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁶, 26, F₂₅, 2, 6) (dual of [(26, 2), 46, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;46,25) [i]
  2. linear OOA(25⁵⁰, 195317, F₂₅, 2, 13) (dual of [(195317, 2), 390584, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁵⁰, 390634, F₂₅, 13) (dual of [390634, 390584, 14]-code), using
      - discarding factors / shortening the dual code based on 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
        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]
        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]
        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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.