MinT - Information on Result #1531475

Information on Result #1531475

Linear OOA(3²³², 4194333, F₃, 3, 21) (dual of [(4194333, 3), 12582767, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³², 4194333, F₃, 2, 21) (dual of [(4194333, 2), 8388434, 22]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²², 32, F₃, 2, 10) (dual of [(32, 2), 42, 11]-NRT-code), using
  - extracting embedded OOA [i] based on digital (12, 22, 32)-net over F₃, using
    - trace code for nets [i] based on digital (1, 11, 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(3²¹⁰, 4194301, F₃, 2, 21) (dual of [(4194301, 2), 8388392, 22]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²¹⁰, 8388602, F₃, 21) (dual of [8388602, 8388392, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹⁰, large, F₃, 21) (dual of [large, large−210, 22]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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(3²³², 2097166, F₃, 5, 21) (dual of [(2097166, 5), 10485598, 22]-NRT-code)	[i]		OOA Folding