MinT - Information on Result #899719

Information on Result #899719

Linear OOA(25⁷³, 195340, F₂₅, 2, 17) (dual of [(195340, 2), 390607, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25⁸, 26, F₂₅, 2, 8) (dual of [(26, 2), 44, 9]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;44,25) [i]
linear OOA(25⁶⁵, 195314, F₂₅, 2, 17) (dual of [(195314, 2), 390563, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁶⁵, 390628, F₂₅, 17) (dual of [390628, 390563, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁶⁵, 390629, F₂₅, 17) (dual of [390629, 390564, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
      1. linear OA(25⁶⁵, 390625, F₂₅, 17) (dual of [390625, 390560, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(25⁶¹, 390625, F₂₅, 16) (dual of [390625, 390564, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(25⁰, 4, F₂₅, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(25⁷³, 48834, F₂₅, 18, 17) (dual of [(48834, 18), 878939, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row