MinT - Information on Result #900434

Information on Result #900434

Linear OOA(27³³, 265750, F₂₇, 2, 8) (dual of [(265750, 2), 531467, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27⁴, 28, F₂₇, 2, 4) (dual of [(28, 2), 52, 5]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;52,27) [i]
linear OOA(27²⁹, 265722, F₂₇, 2, 8) (dual of [(265722, 2), 531415, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27²⁹, 531444, F₂₇, 8) (dual of [531444, 531415, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(27²⁹, 531445, F₂₇, 8) (dual of [531445, 531416, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(27²⁹, 531441, F₂₇, 8) (dual of [531441, 531412, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(27²⁵, 531441, F₂₇, 7) (dual of [531441, 531416, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(27¹⁰⁹, 4460051, F₂₇, 2, 16) (dual of [(4460051, 2), 8919993, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(27³³, 132874, F₂₇, 10, 8) (dual of [(132874, 10), 1328707, 9]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row