MinT - Information on Result #812677

Information on Result #812677

Linear OOA(3⁷¹, 2391491, F₃, 2, 8) (dual of [(2391491, 2), 4782911, 9]-NRT-code), using OOA 2-folding based on linear OA(3⁷¹, 4782982, F₃, 8) (dual of [4782982, 4782911, 9]-code), using

discarding factors / shortening the dual code based on linear OA(3⁷¹, 4782983, F₃, 8) (dual of [4782983, 4782912, 9]-code), using
- constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
  1. linear OA(3⁷¹, 4782969, F₃, 8) (dual of [4782969, 4782898, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
  2. linear OA(3⁵⁷, 4782969, F₃, 7) (dual of [4782969, 4782912, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  3. linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(3⁹⁹, 4782976, F₃, 2, 8) (dual of [(4782976, 2), 9565853, 9]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁰⁰, 4782982, F₃, 2, 8) (dual of [(4782982, 2), 9565864, 9]-NRT-code)	[i]
3	Linear OOA(3²²², 6585792, F₃, 2, 16) (dual of [(6585792, 2), 13171362, 17]-NRT-code)	[i]
4	Linear OOA(3²³⁷, 6585792, F₃, 2, 17) (dual of [(6585792, 2), 13171347, 18]-NRT-code)	[i]
5	Linear OOA(3⁷¹, 2391491, F₃, 3, 8) (dual of [(2391491, 3), 7174402, 9]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
6	Linear OOA(3⁷¹, 2391491, F₃, 4, 8) (dual of [(2391491, 4), 9565893, 9]-NRT-code)	[i]
7	Linear OOA(3⁷¹, 2391491, F₃, 5, 8) (dual of [(2391491, 5), 11957384, 9]-NRT-code)	[i]
8	Digital (63, 71, 2391491)-net over F₃	[i]