MinT - Information on Result #899528

Information on Result #899528

Linear OOA(25⁵⁶, 195343, F₂₅, 2, 13) (dual of [(195343, 2), 390630, 14]-NRT-code), using (u,Â u+v)-construction based on

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]
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
      1. 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]
      2. 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]
      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(25⁵⁶, 65114, F₂₅, 14, 13) (dual of [(65114, 14), 911540, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row