MinT - Information on Result #895348

Information on Result #895348

Linear OOA(3²³⁷, 4194341, F₃, 2, 22) (dual of [(4194341, 2), 8388445, 23]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁶, 40, F₃, 2, 11) (dual of [(40, 2), 54, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 26, 40)-net over F₃, using
  - trace code for nets [i] based on digital (2, 13, 20)-net over F₉, using
    - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
        a function field by GarcÃa and Quoos [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(3²³⁷, 3158054, F₃, 3, 22) (dual of [(3158054, 3), 9473925, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²³⁷, 3158054, F₃, 4, 22) (dual of [(3158054, 4), 12631979, 23]-NRT-code)	[i]
3	Linear OOA(3²³⁷, 3158054, F₃, 5, 22) (dual of [(3158054, 5), 15790033, 23]-NRT-code)	[i]
4	Digital (215, 237, 3158054)-net over F₃	[i]
5	Linear OOA(3²³⁷, 2097170, F₃, 4, 22) (dual of [(2097170, 4), 8388443, 23]-NRT-code)	[i]	OOA Folding