MinT - Information on Result #1612119

Information on Result #1612119

Linear OOA(3²³⁹, 3545220, F₃, 4, 22) (dual of [(3545220, 4), 14180641, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³⁹, 3545220, F₃, 2, 22) (dual of [(3545220, 2), 7090201, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³⁹, 4194357, F₃, 2, 22) (dual of [(4194357, 2), 8388475, 23]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²⁸, 56, F₃, 2, 11) (dual of [(56, 2), 84, 12]-NRT-code), using
    - extracting embedded OOA [i] based on digital (17, 28, 56)-net over F₃, using
      - trace code for nets [i] based on digital (3, 14, 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(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(3²³⁹, 1181739, F₃, 28, 22) (dual of [(1181739, 28), 33088453, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row