MinT - Information on Result #992517

Information on Result #992517

Linear OOA(128⁴⁶, 699051, F₁₂₈, 3, 16) (dual of [(699051, 3), 2097107, 17]-NRT-code), using OOA 3-folding based on linear OA(128⁴⁶, 2097153, F₁₂₈, 16) (dual of [2097153, 2097107, 17]-code), using

discarding factors / shortening the dual code based on linear OA(128⁴⁶, 2097155, F₁₂₈, 16) (dual of [2097155, 2097109, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
  1. linear OA(128⁴⁶, 2097152, F₁₂₈, 16) (dual of [2097152, 2097106, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  2. linear OA(128⁴³, 2097152, F₁₂₈, 15) (dual of [2097152, 2097109, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  3. linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 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(128⁵⁴, 699180, F₁₂₈, 3, 16) (dual of [(699180, 3), 2097486, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(128⁵⁵, 699201, F₁₂₈, 3, 16) (dual of [(699201, 3), 2097548, 17]-NRT-code)	[i]
3	Linear OOA(128⁵⁷, 699243, F₁₂₈, 3, 16) (dual of [(699243, 3), 2097672, 17]-NRT-code)	[i]
4	Linear OOA(128⁵⁸, 699309, F₁₂₈, 3, 16) (dual of [(699309, 3), 2097869, 17]-NRT-code)	[i]
5	Linear OOA(128⁵⁹, 699330, F₁₂₈, 3, 16) (dual of [(699330, 3), 2097931, 17]-NRT-code)	[i]
6	Linear OOA(128⁶⁰, 699351, F₁₂₈, 3, 16) (dual of [(699351, 3), 2097993, 17]-NRT-code)	[i]
7	Linear OOA(128⁶⁰, 699438, F₁₂₈, 3, 16) (dual of [(699438, 3), 2098254, 17]-NRT-code)	[i]
8	Linear OOA(128⁴⁶, 699051, F₁₂₈, 4, 16) (dual of [(699051, 4), 2796158, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
9	Digital (30, 46, 699051)-net over F₁₂₈	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound