MinT - Information on Result #1117859

Information on Result #1117859

Linear OOA(3²³⁴, 1677884, F₃, 5, 20) (dual of [(1677884, 5), 8389186, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁸, 164, F₃, 5, 10) (dual of [(164, 5), 782, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (28, 38, 164)-net over F₃, using
  - trace code for nets [i] based on digital (9, 19, 82)-net over F₉, using
    - base reduction for projective spaces (embedding PG(9,81) in PG(18,9)) for nets [i] based on digital (0, 10, 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(3¹⁹⁶, 1677720, F₃, 5, 20) (dual of [(1677720, 5), 8388404, 21]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁹⁶, 8388600, F₃, 20) (dual of [8388600, 8388404, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁹⁶, large, F₃, 20) (dual of [large, large−196, 21]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²³⁵, 1677884, F₃, 5, 20) (dual of [(1677884, 5), 8389185, 21]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²³⁴, 838941, F₃, 25, 20) (dual of [(838941, 25), 20973291, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row