MinT - Information on Result #899848

Information on Result #899848

Linear OOA(25⁸⁷, 195340, F₂₅, 2, 20) (dual of [(195340, 2), 390593, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁰, 26, F₂₅, 2, 10) (dual of [(26, 2), 42, 11]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;42,25) [i]
linear OOA(25⁷⁷, 195314, F₂₅, 2, 20) (dual of [(195314, 2), 390551, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷⁷, 390628, F₂₅, 20) (dual of [390628, 390551, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁷⁷, 390629, F₂₅, 20) (dual of [390629, 390552, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(25⁷⁷, 390625, F₂₅, 20) (dual of [390625, 390548, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(25⁷³, 390625, F₂₅, 19) (dual of [390625, 390552, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(25⁸⁷, 39067, F₂₅, 22, 20) (dual of [(39067, 22), 859387, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row