MinT - Information on Result #1528611

Information on Result #1528611

Linear OOA(3²⁰⁵, 3845767, F₃, 3, 19) (dual of [(3845767, 3), 11537096, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰⁵, 3845767, F₃, 2, 19) (dual of [(3845767, 2), 7691329, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁰⁵, 4194357, F₃, 2, 19) (dual of [(4194357, 2), 8388509, 20]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²⁴, 56, F₃, 2, 9) (dual of [(56, 2), 88, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (15, 24, 56)-net over F₃, using
      - trace code for nets [i] based on digital (3, 12, 28)-net over F₉, using
        net from sequence [i] based on digital (3, 27)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
        the Hermitian function field over F₉ [i]
  2. linear OOA(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 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: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁰⁵, 1922883, F₃, 5, 19) (dual of [(1922883, 5), 9614210, 20]-NRT-code)	[i]		OOA Folding