MinT - Information on Result #895607

Information on Result #895607

Linear OOA(4¹⁷⁵, 4194815, F₄, 2, 17) (dual of [(4194815, 2), 8389455, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4³⁰, 514, F₄, 2, 8) (dual of [(514, 2), 998, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (22, 30, 514)-net over F₄, using
  - trace code for nets [i] based on digital (7, 15, 257)-net over F₁₆, using
    - base reduction for projective spaces (embedding PG(7,256) in PG(14,16)) for nets [i] based on digital (0, 8, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
linear OOA(4¹⁴⁵, 4194301, F₄, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁴⁵, 8388602, F₄, 17) (dual of [8388602, 8388457, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, large, F₄, 17) (dual of [large, large−145, 18]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁷⁵, 1048703, F₄, 18, 17) (dual of [(1048703, 18), 18876479, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row