MinT - Information on Result #989779

Information on Result #989779

Linear OOA(64⁵¹, 1366, F₆₄, 3, 26) (dual of [(1366, 3), 4047, 27]-NRT-code), using OOA 3-folding based on linear OA(64⁵¹, 4098, F₆₄, 26) (dual of [4098, 4047, 27]-code), using

constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
1. linear OA(64⁵¹, 4096, F₆₄, 26) (dual of [4096, 4045, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
2. linear OA(64⁴⁹, 4096, F₆₄, 25) (dual of [4096, 4047, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(64⁶⁴, 1431, F₆₄, 3, 26) (dual of [(1431, 3), 4229, 27]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁶⁵, 1446, F₆₄, 3, 26) (dual of [(1446, 3), 4273, 27]-NRT-code)	[i]
3	Linear OOA(64⁶⁷, 1470, F₆₄, 3, 26) (dual of [(1470, 3), 4343, 27]-NRT-code)	[i]
4	Linear OOA(64⁶⁹, 1494, F₆₄, 3, 26) (dual of [(1494, 3), 4413, 27]-NRT-code)	[i]
5	Linear OOA(64⁷⁰, 1496, F₆₄, 3, 26) (dual of [(1496, 3), 4418, 27]-NRT-code)	[i]
6	Linear OOA(64⁷¹, 1543, F₆₄, 3, 26) (dual of [(1543, 3), 4558, 27]-NRT-code)	[i]
7	Linear OOA(64⁷⁴, 1550, F₆₄, 3, 26) (dual of [(1550, 3), 4576, 27]-NRT-code)	[i]
8	Linear OOA(64⁷⁴, 1561, F₆₄, 3, 26) (dual of [(1561, 3), 4609, 27]-NRT-code)	[i]
9	Digital (25, 51, 1244)-net over F₆₄	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound