MinT - Information on Result #1117507

Information on Result #1117507

Linear OOA(3¹⁵⁷, 1677804, F₃, 5, 14) (dual of [(1677804, 5), 8388863, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²¹, 84, F₃, 5, 7) (dual of [(84, 5), 399, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 21, 84)-net over F₃, using
  - trace code for nets [i] based on digital (0, 7, 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(3¹³⁶, 1677720, F₃, 5, 14) (dual of [(1677720, 5), 8388464, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹³⁶, 8388600, F₃, 14) (dual of [8388600, 8388464, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹³⁶, large, F₃, 14) (dual of [large, large−136, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁵⁸, 1677804, F₃, 5, 14) (dual of [(1677804, 5), 8388862, 15]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁵⁹, 1677804, F₃, 5, 14) (dual of [(1677804, 5), 8388861, 15]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²⁴⁶, 5033412, F₃, 5, 14) (dual of [(5033412, 5), 25166814, 15]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs