MinT - Information on Result #1466364

Information on Result #1466364

Linear OOA(3¹⁷⁷, 4194442, F₃, 2, 16) (dual of [(4194442, 2), 8388707, 17]-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(3¹⁵¹, 4194301, F₃, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁵¹, 8388602, F₃, 16) (dual of [8388602, 8388451, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁷⁷, 4194442, F₃, 3, 16) (dual of [(4194442, 3), 12583149, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁷⁷, 4194442, F₃, 4, 16) (dual of [(4194442, 4), 16777591, 17]-NRT-code)	[i]
3	Linear OOA(3¹⁷⁷, 4194442, F₃, 5, 16) (dual of [(4194442, 5), 20972033, 17]-NRT-code)	[i]
4	Digital (161, 177, 4194442)-net over F₃	[i]