MinT - Information on Result #989610

Information on Result #989610

Linear OOA(64⁴⁵, 1366, F₆₄, 3, 23) (dual of [(1366, 3), 4053, 24]-NRT-code), using OOA 3-folding based on linear OA(64⁴⁵, 4098, F₆₄, 23) (dual of [4098, 4053, 24]-code), using

constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
1. linear OA(64⁴⁵, 4096, F₆₄, 23) (dual of [4096, 4051, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
2. linear OA(64⁴³, 4096, F₆₄, 22) (dual of [4096, 4053, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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(64⁵⁶, 1431, F₆₄, 3, 23) (dual of [(1431, 3), 4237, 24]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁵⁷, 1446, F₆₄, 3, 23) (dual of [(1446, 3), 4281, 24]-NRT-code)	[i]
3	Linear OOA(64⁵⁹, 1470, F₆₄, 3, 23) (dual of [(1470, 3), 4351, 24]-NRT-code)	[i]
4	Linear OOA(64⁶¹, 1496, F₆₄, 3, 23) (dual of [(1496, 3), 4427, 24]-NRT-code)	[i]
5	Linear OOA(64⁶², 1511, F₆₄, 3, 23) (dual of [(1511, 3), 4471, 24]-NRT-code)	[i]
6	Linear OOA(64⁶³, 1543, F₆₄, 3, 23) (dual of [(1543, 3), 4566, 24]-NRT-code)	[i]
7	Linear OOA(64⁶⁴, 1561, F₆₄, 3, 23) (dual of [(1561, 3), 4619, 24]-NRT-code)	[i]
8	Linear OOA(64⁶⁵, 1576, F₆₄, 3, 23) (dual of [(1576, 3), 4663, 24]-NRT-code)	[i]
9	Digital (22, 45, 1229)-net over F₆₄	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound