MinT - Information on Result #1081344

Information on Result #1081344

Linear OOA(3²⁰⁸, 2097234, F₃, 4, 19) (dual of [(2097234, 4), 8388728, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁷, 84, F₃, 4, 9) (dual of [(84, 4), 309, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (18, 27, 84)-net over F₃, using
  - trace code for nets [i] based on digital (0, 9, 28)-net over F₂₇, using
    - net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
        the rational function field F₂₇(x) [i]
      - Niederreiter sequence [i]
linear OOA(3¹⁸¹, 2097150, F₃, 4, 19) (dual of [(2097150, 4), 8388419, 20]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁸¹, 8388600, F₃, 19) (dual of [8388600, 8388419, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁰⁸, 2097234, F₃, 4, 18) (dual of [(2097234, 4), 8388728, 19]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²⁰⁹, 2097234, F₃, 4, 19) (dual of [(2097234, 4), 8388727, 20]-NRT-code)	[i]		OOA Duplication