MinT - Information on Result #878261

Information on Result #878261

Linear OOA(128¹⁰, 1048577, F₁₂₈, 2, 4) (dual of [(1048577, 2), 2097144, 5]-NRT-code), using OOA 2-folding based on linear OA(128¹⁰, 2097154, F₁₂₈, 4) (dual of [2097154, 2097144, 5]-code), using

discarding factors / shortening the dual code based on linear OA(128¹⁰, 2097155, F₁₂₈, 4) (dual of [2097155, 2097145, 5]-code), using
- constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
  1. linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
  2. linear OA(128⁷, 2097152, F₁₂₈, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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(128¹², 1048706, F₁₂₈, 2, 4) (dual of [(1048706, 2), 2097400, 5]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(128³⁹, 5242878, F₁₂₈, 2, 8) (dual of [(5242878, 2), 10485717, 9]-NRT-code)	[i]
3	Linear OOA(128⁴³, 5242878, F₁₂₈, 2, 9) (dual of [(5242878, 2), 10485713, 10]-NRT-code)	[i]
4	OOA(128³⁶, 5242878, S₁₂₈, 2, 8)	[i]
5	OOA(128³⁹, 5242878, S₁₂₈, 2, 9)	[i]
6	Linear OOA(128¹⁶, large, F₁₂₈, 2, 4)	[i]	Generalized (u,Â u+v)-Construction for OOAs