MinT - Information on Result #1117721

Information on Result #1117721

Linear OOA(3¹⁹³, 1677834, F₃, 5, 17) (dual of [(1677834, 5), 8388977, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁷, 114, F₃, 5, 8) (dual of [(114, 5), 543, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (19, 27, 114)-net over F₃, using
  - trace code for nets [i] based on digital (1, 9, 38)-net over F₂₇, using
    - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
        a function field by SÃ©mirat [i]
linear OOA(3¹⁶⁶, 1677720, F₃, 5, 17) (dual of [(1677720, 5), 8388434, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁶⁶, 8388600, F₃, 17) (dual of [8388600, 8388434, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁹⁴, 1677834, F₃, 5, 17) (dual of [(1677834, 5), 8388976, 18]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁹⁵, 1677834, F₃, 5, 17) (dual of [(1677834, 5), 8388975, 18]-NRT-code)	[i]		OOA Duplication