MinT - Information on Result #895321

Information on Result #895321

Linear OOA(3²³⁴, 4194341, F₃, 2, 21) (dual of [(4194341, 2), 8388448, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁴, 40, F₃, 2, 10) (dual of [(40, 2), 56, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 24, 40)-net over F₃, using
  - trace code for nets [i] based on digital (2, 12, 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(3²¹⁰, 4194301, F₃, 2, 21) (dual of [(4194301, 2), 8388392, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²¹⁰, 8388602, F₃, 21) (dual of [8388602, 8388392, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹⁰, large, F₃, 21) (dual of [large, large−210, 22]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3²³⁵, 4194341, F₃, 2, 21) (dual of [(4194341, 2), 8388447, 22]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²³⁴, 4194341, F₃, 3, 21) (dual of [(4194341, 3), 12582789, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3²³⁴, 4194341, F₃, 4, 21) (dual of [(4194341, 4), 16777130, 22]-NRT-code)	[i]
4	Linear OOA(3²³⁴, 4194341, F₃, 5, 21) (dual of [(4194341, 5), 20971471, 22]-NRT-code)	[i]
5	Digital (213, 234, 4194341)-net over F₃	[i]
6	Linear OOA(3²³⁴, 2097170, F₃, 4, 21) (dual of [(2097170, 4), 8388446, 22]-NRT-code)	[i]	OOA Folding