MinT - Information on Result #895353

Information on Result #895353

Linear OOA(3²⁴⁴, 4194385, F₃, 2, 22) (dual of [(4194385, 2), 8388526, 23]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³³, 84, F₃, 2, 11) (dual of [(84, 2), 135, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (22, 33, 84)-net over F₃, using
  - trace code for nets [i] based on digital (0, 11, 28)-net over F₂₇, using
    - net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
        the rational function field F₂₇(x) [i]
      - Niederreiter sequence [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(3²⁴⁶, 4194386, F₃, 2, 22) (dual of [(4194386, 2), 8388526, 23]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²⁴⁵, 4194385, F₃, 2, 22) (dual of [(4194385, 2), 8388525, 23]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²⁴⁴, 2097192, F₃, 4, 22) (dual of [(2097192, 4), 8388524, 23]-NRT-code)	[i]	OOA Folding