MinT - Information on Result #2486162

Information on Result #2486162

Linear OOA(3¹⁶⁷, 4194324, F₃, 2, 16) (dual of [(4194324, 2), 8388481, 17]-NRT-code), using 1 times NRT-code embedding in larger space 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: Constructive and 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		Method
1	Linear OOA(3¹⁶⁸, 4194324, F₃, 2, 16) (dual of [(4194324, 2), 8388480, 17]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁶⁷, 3222139, F₃, 3, 16) (dual of [(3222139, 3), 9666250, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3¹⁶⁷, 3222139, F₃, 4, 16) (dual of [(3222139, 4), 12888389, 17]-NRT-code)	[i]
4	Linear OOA(3¹⁶⁷, 3222139, F₃, 5, 16) (dual of [(3222139, 5), 16110528, 17]-NRT-code)	[i]
5	Digital (151, 167, 3222139)-net over F₃	[i]
6	Linear OOA(3¹⁶⁷, 2097162, F₃, 4, 16) (dual of [(2097162, 4), 8388481, 17]-NRT-code)	[i]	OOA Folding