MinT - Information on Result #1606316

Information on Result #1606316

Linear OOA(3¹⁶⁹, 3815468, F₃, 4, 16) (dual of [(3815468, 4), 15261703, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁹, 3815468, F₃, 2, 16) (dual of [(3815468, 2), 7630767, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁹, 4194333, F₃, 2, 16) (dual of [(4194333, 2), 8388497, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁸, 32, F₃, 2, 8) (dual of [(32, 2), 46, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (10, 18, 32)-net over F₃, using
      - trace code for nets [i] based on digital (1, 9, 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(3¹⁵¹, 4194301, F₃, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁵¹, 8388602, F₃, 16) (dual of [8388602, 8388451, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(3¹⁶⁹, 1907733, F₃, 20, 16) (dual of [(1907733, 20), 38154491, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row