MinT - Information on Result #895609

Information on Result #895609

Linear OOA(4¹⁷⁷, 4195329, F₄, 2, 17) (dual of [(4195329, 2), 8390481, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4³², 1028, F₄, 2, 8) (dual of [(1028, 2), 2024, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (24, 32, 1028)-net over F₄, using
  - trace code 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		Method
1	Linear OOA(4¹⁷⁷, 4195329, F₄, 2, 16) (dual of [(4195329, 2), 8390481, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4¹⁷⁹, 4195330, F₄, 2, 17) (dual of [(4195330, 2), 8390481, 18]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(4¹⁷⁸, 4195329, F₄, 2, 17) (dual of [(4195329, 2), 8390480, 18]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(4¹⁷⁷, 1048832, F₄, 18, 17) (dual of [(1048832, 18), 18878799, 18]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row