MinT - Information on Result #899480

Information on Result #899480

Linear OOA(25⁵¹, 195340, F₂₅, 2, 12) (dual of [(195340, 2), 390629, 13]-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(25⁴⁵, 195314, F₂₅, 2, 12) (dual of [(195314, 2), 390583, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁴⁵, 390628, F₂₅, 12) (dual of [390628, 390583, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁴⁵, 390629, F₂₅, 12) (dual of [390629, 390584, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(25⁴⁵, 390625, F₂₅, 12) (dual of [390625, 390580, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(25⁴¹, 390625, F₂₅, 11) (dual of [390625, 390584, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(25⁵¹, 65113, F₂₅, 14, 12) (dual of [(65113, 14), 911531, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row