MinT - Information on Result #1525472

Information on Result #1525472

Linear OOA(3¹⁶⁸, 3506276, F₃, 3, 16) (dual of [(3506276, 3), 10518660, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁸, 3506276, F₃, 2, 16) (dual of [(3506276, 2), 7012384, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁸, 4194324, F₃, 2, 16) (dual of [(4194324, 2), 8388480, 17]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁶⁷, 4194324, F₃, 2, 16) (dual of [(4194324, 2), 8388481, 17]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁶⁵, 4194323, F₃, 2, 16) (dual of [(4194323, 2), 8388481, 17]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(3¹⁴, 22, F₃, 2, 8) (dual of [(22, 2), 30, 9]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 14, 22)-net over F₃, using
        linear code embedding found in a computer search [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(3¹⁶⁸, 1753138, F₃, 5, 16) (dual of [(1753138, 5), 8765522, 17]-NRT-code)	[i]		OOA Folding