MinT - Information on Result #1117814

Information on Result #1117814

Linear OOA(3²²¹, 1678120, F₃, 5, 19) (dual of [(1678120, 5), 8390379, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁴⁰, 400, F₃, 5, 9) (dual of [(400, 5), 1960, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (31, 40, 400)-net over F₃, using
  - trace code for nets [i] based on digital (1, 10, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
linear OOA(3¹⁸¹, 1677720, F₃, 5, 19) (dual of [(1677720, 5), 8388419, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁸¹, 8388600, F₃, 19) (dual of [8388600, 8388419, 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		This result only	Method
1	Linear OOA(3²²¹, 1678120, F₃, 5, 18) (dual of [(1678120, 5), 8390379, 19]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²², 1678120, F₃, 5, 19) (dual of [(1678120, 5), 8390378, 20]-NRT-code)	[i]		OOA Duplication