MinT - Information on Result #1081076

Information on Result #1081076

Linear OOA(3¹³⁹, 2097234, F₃, 4, 13) (dual of [(2097234, 4), 8388797, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁸, 84, F₃, 4, 6) (dual of [(84, 4), 318, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 18, 84)-net over F₃, using
  - trace code for nets [i] based on digital (0, 6, 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(3¹²¹, 2097150, F₃, 4, 13) (dual of [(2097150, 4), 8388479, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹²¹, 8388600, F₃, 13) (dual of [8388600, 8388479, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹³⁹, 2097234, F₃, 4, 12) (dual of [(2097234, 4), 8388797, 13]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁴⁰, 2097234, F₃, 4, 13) (dual of [(2097234, 4), 8388796, 14]-NRT-code)	[i]		OOA Duplication