MinT - Information on Result #1466375

Information on Result #1466375

Linear OOA(3¹⁹⁰, 4194397, F₃, 2, 17) (dual of [(4194397, 2), 8388604, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁴, 96, F₃, 2, 8) (dual of [(96, 2), 168, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁴, 96, F₃, 8) (dual of [96, 72, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴, 99, F₃, 8) (dual of [99, 75, 9]-code), using
    - a â€œXBâ€ code from Brouwerâ€™s database [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(3¹⁹⁰, 4194397, F₃, 3, 17) (dual of [(4194397, 3), 12583001, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁹⁰, 4194397, F₃, 4, 17) (dual of [(4194397, 4), 16777398, 18]-NRT-code)	[i]
3	Linear OOA(3¹⁹⁰, 4194397, F₃, 5, 17) (dual of [(4194397, 5), 20971795, 18]-NRT-code)	[i]
4	Digital (173, 190, 4194397)-net over F₃	[i]