MinT - Information on Result #1590208

Information on Result #1590208

Linear OOA(2¹⁰⁷, 4194452, F₂, 4, 8) (dual of [(4194452, 4), 16777701, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁰⁷, 4194452, F₂, 2, 8) (dual of [(4194452, 2), 8388797, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹⁵, 151, F₂, 2, 4) (dual of [(151, 2), 287, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(2¹⁵, 151, F₂, 4) (dual of [151, 136, 5]-code), using
    - a â€œGBâ€ code from Brouwerâ€™s database [i]
2. linear OOA(2⁹², 4194301, F₂, 2, 8) (dual of [(4194301, 2), 8388510, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2⁹², 8388602, F₂, 8) (dual of [8388602, 8388510, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁹², large, F₂, 8) (dual of [large, large−92, 9]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁰⁷, 4194451, F₂, 5, 8) (dual of [(4194451, 5), 20972148, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁰⁷, 4194451, F₂, 6, 8) (dual of [(4194451, 6), 25166599, 9]-NRT-code)	[i]
3	Linear OOA(2¹⁰⁷, 4194451, F₂, 7, 8) (dual of [(4194451, 7), 29361050, 9]-NRT-code)	[i]
4	Linear OOA(2¹⁰⁷, 4194451, F₂, 8, 8) (dual of [(4194451, 8), 33555501, 9]-NRT-code)	[i]