MinT - Information on Result #1590073

Information on Result #1590073

Linear OOA(2¹⁰³, 2731713, F₂, 4, 9) (dual of [(2731713, 4), 10926749, 10]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁰³, 2731713, F₂, 3, 9) (dual of [(2731713, 3), 8195036, 10]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁰³, 2796233, F₂, 3, 9) (dual of [(2796233, 3), 8388596, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 32, F₂, 3, 4) (dual of [(32, 3), 86, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 10, 32)-net over F₂, using
      - linear code embedding found in a computer search [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(2¹⁰³, 2731712, F₂, 5, 9) (dual of [(2731712, 5), 13658457, 10]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁰³, 2731712, F₂, 6, 9) (dual of [(2731712, 6), 16390169, 10]-NRT-code)	[i]
3	Linear OOA(2¹⁰³, 2731712, F₂, 7, 9) (dual of [(2731712, 7), 19121881, 10]-NRT-code)	[i]
4	Linear OOA(2¹⁰³, 2731712, F₂, 8, 9) (dual of [(2731712, 8), 21853593, 10]-NRT-code)	[i]