MinT - Information on Result #856702

Information on Result #856702

Linear OOA(16⁸⁶, 524290, F₁₆, 2, 19) (dual of [(524290, 2), 1048494, 20]-NRT-code), using OOA 2-folding based on linear OA(16⁸⁶, 1048580, F₁₆, 19) (dual of [1048580, 1048494, 20]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸⁶, 1048581, F₁₆, 19) (dual of [1048581, 1048495, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
  1. linear OA(16⁸⁶, 1048576, F₁₆, 19) (dual of [1048576, 1048490, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. linear OA(16⁸¹, 1048576, F₁₆, 18) (dual of [1048576, 1048495, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
  3. linear OA(16⁰, 5, F₁₆, 0) (dual of [5, 5, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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(16⁹⁶, 524314, F₁₆, 2, 19) (dual of [(524314, 2), 1048532, 20]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(16⁹⁷, 524323, F₁₆, 2, 19) (dual of [(524323, 2), 1048549, 20]-NRT-code)	[i]
3	Linear OOA(16⁹⁸, 524328, F₁₆, 2, 19) (dual of [(524328, 2), 1048558, 20]-NRT-code)	[i]
4	Linear OOA(16⁹⁹, 524335, F₁₆, 2, 19) (dual of [(524335, 2), 1048571, 20]-NRT-code)	[i]
5	Linear OOA(16¹⁰⁰, 524339, F₁₆, 2, 19) (dual of [(524339, 2), 1048578, 20]-NRT-code)	[i]
6	Linear OOA(16¹⁰¹, 524355, F₁₆, 2, 19) (dual of [(524355, 2), 1048609, 20]-NRT-code)	[i]
7	Digital (67, 86, 524290)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound