MinT - Information on Result #895239

Information on Result #895239

Linear OOA(3²¹⁴, 4194465, F₃, 2, 18) (dual of [(4194465, 2), 8388716, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁴, 164, F₃, 2, 9) (dual of [(164, 2), 294, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (25, 34, 164)-net over F₃, using
  - trace code for nets [i] based on digital (8, 17, 82)-net over F₉, using
    - base reduction for projective spaces (embedding PG(8,81) in PG(16,9)) for nets [i] based on digital (0, 9, 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(3¹⁸⁰, 4194301, F₃, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸⁰, 8388602, F₃, 18) (dual of [8388602, 8388422, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁴, 2097232, F₃, 4, 18) (dual of [(2097232, 4), 8388714, 19]-NRT-code)	[i]		OOA Folding