MinT - Information on Result #895604

Information on Result #895604

Linear OOA(4¹⁶⁹, 4194496, F₄, 2, 17) (dual of [(4194496, 2), 8388823, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁴, 195, F₄, 2, 8) (dual of [(195, 2), 366, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 24, 195)-net over F₄, using
  - trace code for nets [i] based on digital (0, 8, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(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(4¹⁶⁹, 4194496, F₄, 2, 16) (dual of [(4194496, 2), 8388823, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4¹⁷¹, 4194497, F₄, 2, 17) (dual of [(4194497, 2), 8388823, 18]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(4¹⁷⁰, 4194496, F₄, 2, 17) (dual of [(4194496, 2), 8388822, 18]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(4¹⁶⁹, 1048623, F₄, 18, 17) (dual of [(1048623, 18), 18875045, 18]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row