MinT - Information on Result #895600

Information on Result #895600

Linear OOA(4¹⁶¹, 4194335, F₄, 2, 17) (dual of [(4194335, 2), 8388509, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹⁶, 34, F₄, 2, 8) (dual of [(34, 2), 52, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 16, 34)-net over F₄, using
  - trace code for nets [i] based on digital (0, 8, 17)-net over F₁₆, using
    - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
        the rational function field F₁₆(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(4¹⁶¹, 4194335, F₄, 2, 16) (dual of [(4194335, 2), 8388509, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4¹⁶², 4194335, F₄, 2, 17) (dual of [(4194335, 2), 8388508, 18]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4¹⁶¹, 1048583, F₄, 18, 17) (dual of [(1048583, 18), 18874333, 18]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row