MinT - Information on Result #895350

Information on Result #895350

Linear OOA(3²³⁹, 4194357, F₃, 2, 22) (dual of [(4194357, 2), 8388475, 23]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁸, 56, F₃, 2, 11) (dual of [(56, 2), 84, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (17, 28, 56)-net over F₃, using
  - trace code for nets [i] based on digital (3, 14, 28)-net over F₉, using
    - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
        the Hermitian function field over F₉ [i]
linear OOA(3²¹¹, 4194301, F₃, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²¹¹, 8388602, F₃, 22) (dual of [8388602, 8388391, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹¹, large, F₃, 22) (dual of [large, large−211, 23]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁴⁰, 4194357, F₃, 2, 22) (dual of [(4194357, 2), 8388474, 23]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²³⁹, 3545220, F₃, 3, 22) (dual of [(3545220, 3), 10635421, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3²³⁹, 3545220, F₃, 4, 22) (dual of [(3545220, 4), 14180641, 23]-NRT-code)	[i]
4	Linear OOA(3²³⁹, 3545220, F₃, 5, 22) (dual of [(3545220, 5), 17725861, 23]-NRT-code)	[i]
5	Digital (217, 239, 3545220)-net over F₃	[i]
6	Linear OOA(3²³⁹, 2097178, F₃, 4, 22) (dual of [(2097178, 4), 8388473, 23]-NRT-code)	[i]	OOA Folding