MinT - Information on Result #2486678

Information on Result #2486678

Linear OOA(3²³⁶, 4194333, F₃, 2, 22) (dual of [(4194333, 2), 8388430, 23]-NRT-code), using 3¹ times duplication based on linear OOA(3²³⁵, 4194333, F₃, 2, 22) (dual of [(4194333, 2), 8388431, 23]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁴, 32, F₃, 2, 11) (dual of [(32, 2), 40, 12]-NRT-code), using
  - extracting embedded OOA [i] based on digital (13, 24, 32)-net over F₃, using
    - trace code for nets [i] based on digital (1, 12, 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(3²¹¹, 4194301, F₃, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²¹¹, 8388602, F₃, 22) (dual of [8388602, 8388391, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹¹, large, F₃, 22) (dual of [large, large−211, 23]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(3²³⁶, 2980628, F₃, 3, 22) (dual of [(2980628, 3), 8941648, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²³⁶, 2980628, F₃, 4, 22) (dual of [(2980628, 4), 11922276, 23]-NRT-code)	[i]
3	Linear OOA(3²³⁶, 2980628, F₃, 5, 22) (dual of [(2980628, 5), 14902904, 23]-NRT-code)	[i]
4	Digital (214, 236, 2980628)-net over F₃	[i]