MinT - Information on Result #874224

Information on Result #874224

Linear OOA(64⁶¹, 131073, F₆₄, 2, 21) (dual of [(131073, 2), 262085, 22]-NRT-code), using OOA 2-folding based on linear OA(64⁶¹, 262146, F₆₄, 21) (dual of [262146, 262085, 22]-code), using

discarding factors / shortening the dual code based on linear OA(64⁶¹, 262147, F₆₄, 21) (dual of [262147, 262086, 22]-code), using
- constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
  1. linear OA(64⁶¹, 262144, F₆₄, 21) (dual of [262144, 262083, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
  2. linear OA(64⁵⁸, 262144, F₆₄, 20) (dual of [262144, 262086, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
  3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 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(64⁷¹, 131138, F₆₄, 2, 21) (dual of [(131138, 2), 262205, 22]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁷², 131153, F₆₄, 2, 21) (dual of [(131153, 2), 262234, 22]-NRT-code)	[i]
3	Linear OOA(64⁷⁴, 131177, F₆₄, 2, 21) (dual of [(131177, 2), 262280, 22]-NRT-code)	[i]
4	Linear OOA(64⁷⁶, 131203, F₆₄, 2, 21) (dual of [(131203, 2), 262330, 22]-NRT-code)	[i]
5	Linear OOA(64⁷⁷, 131218, F₆₄, 2, 21) (dual of [(131218, 2), 262359, 22]-NRT-code)	[i]
6	Linear OOA(64⁷⁸, 131250, F₆₄, 2, 21) (dual of [(131250, 2), 262422, 22]-NRT-code)	[i]
7	Linear OOA(64⁶¹, 99772, F₆₄, 3, 21) (dual of [(99772, 3), 299255, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
8	Digital (40, 61, 99772)-net over F₆₄	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound