MinT - Information on Result #1590173

Information on Result #1590173

Linear OOA(2¹⁰⁶, 2796282, F₂, 4, 9) (dual of [(2796282, 4), 11185022, 10]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁰⁶, 2796282, F₂, 3, 9) (dual of [(2796282, 3), 8388740, 10]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹³, 81, F₂, 3, 4) (dual of [(81, 3), 230, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(2¹³, 81, F₂, 4) (dual of [81, 68, 5]-code), using
    - 1 times truncation [i] based on linear OA(2¹⁴, 82, F₂, 5) (dual of [82, 68, 6]-code), using
      - a â€œSh1â€ code from Brouwerâ€™s database [i]
2. linear OOA(2⁹³, 2796201, F₂, 3, 9) (dual of [(2796201, 3), 8388510, 10]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁹³, large, F₂, 9) (dual of [large, large−93, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [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(2¹⁰⁶, 2796281, F₂, 5, 9) (dual of [(2796281, 5), 13981299, 10]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁰⁶, 2796281, F₂, 6, 9) (dual of [(2796281, 6), 16777580, 10]-NRT-code)	[i]
3	Linear OOA(2¹⁰⁶, 2796281, F₂, 7, 9) (dual of [(2796281, 7), 19573861, 10]-NRT-code)	[i]
4	Linear OOA(2¹⁰⁶, 2796281, F₂, 8, 9) (dual of [(2796281, 8), 22370142, 10]-NRT-code)	[i]