MinT - Information on Result #894901

Information on Result #894901

Linear OOA(3⁶⁶, 4194321, F₃, 2, 7) (dual of [(4194321, 2), 8388576, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
  - doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
    - ovoid in PG(3,Â 3) [i]
linear OOA(3⁶¹, 4194301, F₃, 2, 7) (dual of [(4194301, 2), 8388541, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁶¹, 8388602, F₃, 7) (dual of [8388602, 8388541, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3⁶⁶, 4194321, F₃, 3, 7) (dual of [(4194321, 3), 12582897, 8]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3⁶⁶, 4194321, F₃, 4, 7) (dual of [(4194321, 4), 16777218, 8]-NRT-code)	[i]
3	Linear OOA(3⁶⁶, 4194321, F₃, 5, 7) (dual of [(4194321, 5), 20971539, 8]-NRT-code)	[i]
4	Digital (59, 66, 4194321)-net over F₃	[i]