MinT - Information on Result #1466381

Information on Result #1466381

Linear OOA(3²⁰³, 4194350, F₃, 2, 18) (dual of [(4194350, 2), 8388497, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²³, 49, F₃, 2, 9) (dual of [(49, 2), 75, 10]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²³, 49, F₃, 9) (dual of [49, 26, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²³, 53, F₃, 9) (dual of [53, 30, 10]-code), using
    - 7 times truncation [i] based on linear OA(3³⁰, 60, F₃, 16) (dual of [60, 30, 17]-code), using
      - strength reduction [i] based on linear OA(3³⁰, 60, F₃, 17) (dual of [60, 30, 18]-code), using
        extended quadratic residue code Q_e(60,3) [i]
linear OOA(3¹⁸⁰, 4194301, F₃, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸⁰, 8388602, F₃, 18) (dual of [8388602, 8388422, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁰³, 4194350, F₃, 3, 18) (dual of [(4194350, 3), 12582847, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁰³, 4194350, F₃, 4, 18) (dual of [(4194350, 4), 16777197, 19]-NRT-code)	[i]
3	Linear OOA(3²⁰³, 4194350, F₃, 5, 18) (dual of [(4194350, 5), 20971547, 19]-NRT-code)	[i]
4	Digital (185, 203, 4194350)-net over F₃	[i]