MinT - Information on Result #1612311

Information on Result #1612311

Linear OOA(3²⁴¹, 3979850, F₃, 4, 22) (dual of [(3979850, 4), 15919159, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴¹, 3979850, F₃, 2, 22) (dual of [(3979850, 2), 7959459, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴¹, 4194361, F₃, 2, 22) (dual of [(4194361, 2), 8388481, 23]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3³⁰, 60, F₃, 2, 11) (dual of [(60, 2), 90, 12]-NRT-code), using
    - extracting embedded OOA [i] based on digital (19, 30, 60)-net over F₃, using
      - trace code for nets [i] based on digital (4, 15, 30)-net over F₉, using
        net from sequence [i] based on digital (4, 29)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
        a function field by SÃ©mirat [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: 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(3²⁴¹, 1326616, F₃, 28, 22) (dual of [(1326616, 28), 37145007, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row