MinT - Information on Result #895264

Information on Result #895264

Linear OOA(3²⁰⁸, 4194385, F₃, 2, 19) (dual of [(4194385, 2), 8388562, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁷, 84, F₃, 2, 9) (dual of [(84, 2), 141, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (18, 27, 84)-net over F₃, using
  - trace code for nets [i] based on digital (0, 9, 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(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁰⁸, 4194385, F₃, 2, 18) (dual of [(4194385, 2), 8388562, 19]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²¹⁰, 4194386, F₃, 2, 19) (dual of [(4194386, 2), 8388562, 20]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3²⁰⁹, 4194385, F₃, 2, 19) (dual of [(4194385, 2), 8388561, 20]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3²⁰⁸, 2097192, F₃, 4, 19) (dual of [(2097192, 4), 8388560, 20]-NRT-code)	[i]	OOA Folding