MinT - Information on Result #899362

Information on Result #899362

Linear OOA(25²⁸, 195340, F₂₅, 2, 7) (dual of [(195340, 2), 390652, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25³, 26, F₂₅, 2, 3) (dual of [(26, 2), 49, 4]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;49,25) [i]
linear OOA(25²⁵, 195314, F₂₅, 2, 7) (dual of [(195314, 2), 390603, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25²⁵, 390628, F₂₅, 7) (dual of [390628, 390603, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(25²⁵, 390629, F₂₅, 7) (dual of [390629, 390604, 8]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
      1. linear OA(25²⁵, 390625, F₂₅, 7) (dual of [390625, 390600, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(25²¹, 390625, F₂₅, 6) (dual of [390625, 390604, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(25⁹⁴, 4389641, F₂₅, 2, 14) (dual of [(4389641, 2), 8779188, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(25⁹⁹, 4389641, F₂₅, 2, 15) (dual of [(4389641, 2), 8779183, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs