MinT - Information on Result #899959

Information on Result #899959

Linear OOA(25¹⁰², 195344, F₂₅, 2, 23) (dual of [(195344, 2), 390586, 24]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹², 27, F₂₅, 2, 11) (dual of [(27, 2), 42, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 12, 27)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
    - Niederreiter sequence [i]
linear OOA(25⁹⁰, 195317, F₂₅, 2, 23) (dual of [(195317, 2), 390544, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁹⁰, 390634, F₂₅, 23) (dual of [390634, 390544, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁹⁰, 390635, F₂₅, 23) (dual of [390635, 390545, 24]-code), using
    - constructionÂ X applied to C([0,11]) âŠ‚ C([0,10]) [i] based on
      1. linear OA(25⁸⁹, 390626, F₂₅, 23) (dual of [390626, 390537, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
      2. 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]
      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.