MinT - Information on Result #900872

Information on Result #900872

Linear OOA(27⁸⁷, 265750, F₂₇, 2, 20) (dual of [(265750, 2), 531413, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27¹⁰, 28, F₂₇, 2, 10) (dual of [(28, 2), 46, 11]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;46,27) [i]
linear OOA(27⁷⁷, 265722, F₂₇, 2, 20) (dual of [(265722, 2), 531367, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁷⁷, 531444, F₂₇, 20) (dual of [531444, 531367, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁷⁷, 531445, F₂₇, 20) (dual of [531445, 531368, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(27⁷⁷, 531441, F₂₇, 20) (dual of [531441, 531364, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(27⁷³, 531441, F₂₇, 19) (dual of [531441, 531368, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(27⁰, 4, F₂₇, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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(27⁸⁷, 53149, F₂₇, 22, 20) (dual of [(53149, 22), 1169191, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row