MinT - Information on Result #1009326

Information on Result #1009326

Linear OOA(2²³⁸, 5592412, F₂, 3, 15) (dual of [(5592412, 3), 16776998, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
- OOAs constructed from BCH codes [i]
linear OOA(2¹⁷⁰, 2796206, F₂, 3, 15) (dual of [(2796206, 3), 8388448, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁸, 5, F₂, 3, 7) (dual of [(5, 3), 7, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁶², 2796201, F₂, 3, 15) (dual of [(2796201, 3), 8388441, 16]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²³⁸, 5592412, F₂, 4, 15) (dual of [(5592412, 4), 22369410, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³⁸, 5592412, F₂, 5, 15) (dual of [(5592412, 5), 27961822, 16]-NRT-code)	[i]
3	Linear OOA(2²³⁸, 5592412, F₂, 6, 15) (dual of [(5592412, 6), 33554234, 16]-NRT-code)	[i]
4	Linear OOA(2²³⁸, 5592412, F₂, 7, 15) (dual of [(5592412, 7), 39146646, 16]-NRT-code)	[i]
5	Linear OOA(2²³⁸, 5592412, F₂, 8, 15) (dual of [(5592412, 8), 44739058, 16]-NRT-code)	[i]
6	Digital (223, 238, 5592412)-net over F₂	[i]
7	Linear OOA(2²³⁸, 2796206, F₂, 5, 15) (dual of [(2796206, 5), 13980792, 16]-NRT-code)	[i]	OOA Folding
8	Linear OOA(2²³⁸, 2796206, F₂, 6, 15) (dual of [(2796206, 6), 16776998, 16]-NRT-code)	[i]	OOA Folding