MinT - Information on Result #861096

Information on Result #861096

Linear OOA(25⁶³, 195327, F₂₅, 2, 15) (dual of [(195327, 2), 390591, 16]-NRT-code), using OOA 2-folding based on linear OA(25⁶³, 390654, F₂₅, 15) (dual of [390654, 390591, 16]-code), using

discarding factors / shortening the dual code based on linear OA(25⁶³, 390655, F₂₅, 15) (dual of [390655, 390592, 16]-code), using
- constructionÂ X applied to C([0,7]) âŠ‚ C([0,4]) [i] based on
  1. 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]
  2. linear OA(25³³, 390626, F₂₅, 9) (dual of [390626, 390593, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  3. linear OA(25⁶, 29, F₂₅, 5) (dual of [29, 23, 6]-code), using
    - construction for [s,Â sâˆ’6,Â 6]-code from [s,Â 3,Â sâˆ’3]-code [i] based on linear OA(25²⁶, 29, F₂₅, 25) (dual of [29, 3, 26]-code), using
      - constructionÂ X applied to C₁ âŠ‚ C₀ [i] based on
        linear OA(25²⁵, 26, F₂₅, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,25)), using code C₁ for uÂ =Â 2 by de Boer and Brouwer [i]
        linear OA(25²³, 26, F₂₅, 23) (dual of [26, 3, 24]-code or 26-arc in PG(22,25)), using code C₀ for uÂ =Â 2 by de Boer and Brouwer [i]
        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]

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.