MinT - Information on Result #2486413

Information on Result #2486413

Linear OOA(3²⁰², 4194333, F₃, 2, 19) (dual of [(4194333, 2), 8388464, 20]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁰¹, 4194333, F₃, 2, 19) (dual of [(4194333, 2), 8388465, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁰, 32, F₃, 2, 9) (dual of [(32, 2), 44, 10]-NRT-code), using
  - extracting embedded OOA [i] based on digital (11, 20, 32)-net over F₃, using
    - trace code for nets [i] based on digital (1, 10, 16)-net over F₉, using
      - net from sequence [i] based on digital (1, 15)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
        a function field by GarcÃa and Quoos [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: Constructive and 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		Method
1	Linear OOA(3²⁰², 3129841, F₃, 3, 19) (dual of [(3129841, 3), 9389321, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁰², 3129841, F₃, 4, 19) (dual of [(3129841, 4), 12519162, 20]-NRT-code)	[i]
3	Linear OOA(3²⁰², 3129841, F₃, 5, 19) (dual of [(3129841, 5), 15649003, 20]-NRT-code)	[i]
4	Digital (183, 202, 3129841)-net over F₃	[i]