MinT - Information on Result #1466391

Information on Result #1466391

Linear OOA(3²⁰⁹, 4194413, F₃, 2, 19) (dual of [(4194413, 2), 8388617, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁸, 112, F₃, 2, 9) (dual of [(112, 2), 196, 10]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁸, 112, F₃, 9) (dual of [112, 84, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁸, 125, F₃, 9) (dual of [125, 97, 10]-code), using
    - a â€œBZâ€ code from Brouwerâ€™s database [i]
linear OOA(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁰⁹, 4194413, F₃, 3, 19) (dual of [(4194413, 3), 12583030, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁰⁹, 4194413, F₃, 4, 19) (dual of [(4194413, 4), 16777443, 20]-NRT-code)	[i]
3	Linear OOA(3²⁰⁹, 4194413, F₃, 5, 19) (dual of [(4194413, 5), 20971856, 20]-NRT-code)	[i]
4	Digital (190, 209, 4194413)-net over F₃	[i]