MinT - Information on Result #1466377

Information on Result #1466377

Linear OOA(3¹⁹², 4194442, F₃, 2, 17) (dual of [(4194442, 2), 8388692, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁶, 141, F₃, 2, 8) (dual of [(141, 2), 256, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁶, 141, F₃, 8) (dual of [141, 115, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁶, 242, F₃, 8) (dual of [242, 216, 9]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(3¹⁶⁶, 4194301, F₃, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶⁶, 8388602, F₃, 17) (dual of [8388602, 8388436, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁹², 4194442, F₃, 3, 17) (dual of [(4194442, 3), 12583134, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁹², 4194442, F₃, 4, 17) (dual of [(4194442, 4), 16777576, 18]-NRT-code)	[i]
3	Linear OOA(3¹⁹², 4194442, F₃, 5, 17) (dual of [(4194442, 5), 20972018, 18]-NRT-code)	[i]
4	Digital (175, 192, 4194442)-net over F₃	[i]