MinT - Information on Result #1466372

Information on Result #1466372

Linear OOA(3¹⁸⁷, 4194355, F₃, 2, 17) (dual of [(4194355, 2), 8388523, 18]-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(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(3¹⁸⁷, 4194355, F₃, 3, 17) (dual of [(4194355, 3), 12582878, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸⁷, 4194355, F₃, 4, 17) (dual of [(4194355, 4), 16777233, 18]-NRT-code)	[i]
3	Linear OOA(3¹⁸⁷, 4194355, F₃, 5, 17) (dual of [(4194355, 5), 20971588, 18]-NRT-code)	[i]
4	Digital (170, 187, 4194355)-net over F₃	[i]