MinT - Information on Result #1117400

Information on Result #1117400

Linear OOA(3¹⁴³, 1677884, F₃, 5, 13) (dual of [(1677884, 5), 8389277, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²², 164, F₃, 5, 6) (dual of [(164, 5), 798, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 22, 164)-net over F₃, using
  - trace code for nets [i] based on digital (5, 11, 82)-net over F₉, using
    - base reduction for projective spaces (embedding PG(5,81) in PG(10,9)) for nets [i] based on digital (0, 6, 82)-net over F₈₁, using
      - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
linear OOA(3¹²¹, 1677720, F₃, 5, 13) (dual of [(1677720, 5), 8388479, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹²¹, 8388600, F₃, 13) (dual of [8388600, 8388479, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁴³, 1677884, F₃, 5, 12) (dual of [(1677884, 5), 8389277, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁴⁴, 1677884, F₃, 5, 13) (dual of [(1677884, 5), 8389276, 14]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²³¹, 5033652, F₃, 5, 13) (dual of [(5033652, 5), 25168029, 14]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs