MinT - Information on Result #1466359

Information on Result #1466359

Linear OOA(3¹⁷², 4194355, F₃, 2, 16) (dual of [(4194355, 2), 8388538, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²¹, 54, F₃, 2, 8) (dual of [(54, 2), 87, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²¹, 54, F₃, 8) (dual of [54, 33, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹, 80, F₃, 8) (dual of [80, 59, 9]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’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(3¹⁷², 4194355, F₃, 3, 16) (dual of [(4194355, 3), 12582893, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁷², 4194355, F₃, 4, 16) (dual of [(4194355, 4), 16777248, 17]-NRT-code)	[i]
3	Linear OOA(3¹⁷², 4194355, F₃, 5, 16) (dual of [(4194355, 5), 20971603, 17]-NRT-code)	[i]
4	Digital (156, 172, 4194355)-net over F₃	[i]