MinT - Information on Result #1466398

Information on Result #1466398

Linear OOA(3²¹⁶, 4194646, F₃, 2, 19) (dual of [(4194646, 2), 8389076, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁵, 345, F₃, 2, 9) (dual of [(345, 2), 655, 10]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3³⁵, 345, F₃, 9) (dual of [345, 310, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³⁵, 364, F₃, 9) (dual of [364, 329, 10]-code), using
    - 1 times truncation [i] based on linear OA(3³⁶, 365, F₃, 10) (dual of [365, 329, 11]-code), using
      - the BCH-code C(I) with length 365Â | 3¹²âˆ’1, defining interval IÂ =Â {−9,−7,−5,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(3²¹⁶, 4194646, F₃, 3, 19) (dual of [(4194646, 3), 12583722, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²¹⁶, 4194646, F₃, 4, 19) (dual of [(4194646, 4), 16778368, 20]-NRT-code)	[i]
3	Linear OOA(3²¹⁶, 4194646, F₃, 5, 19) (dual of [(4194646, 5), 20973014, 20]-NRT-code)	[i]
4	Digital (197, 216, 4194646)-net over F₃	[i]
5	Linear OOA(3²¹⁶, 2097323, F₃, 4, 19) (dual of [(2097323, 4), 8389076, 20]-NRT-code)	[i]	OOA Folding