MinT - Information on Result #900029

Information on Result #900029

Linear OOA(25¹¹⁰, 195343, F₂₅, 2, 25) (dual of [(195343, 2), 390576, 26]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹², 26, F₂₅, 2, 12) (dual of [(26, 2), 40, 13]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;40,25) [i]
linear OOA(25⁹⁸, 195317, F₂₅, 2, 25) (dual of [(195317, 2), 390536, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁹⁸, 390634, F₂₅, 25) (dual of [390634, 390536, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁹⁸, 390635, F₂₅, 25) (dual of [390635, 390537, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,11]) [i] based on
      1. linear OA(25⁹⁷, 390626, F₂₅, 25) (dual of [390626, 390529, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. 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]
      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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(25¹¹⁰, 32557, F₂₅, 26, 25) (dual of [(32557, 26), 846372, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row