MinT - Information on Result #856636

Information on Result #856636

Linear OOA(16⁸¹, 524290, F₁₆, 2, 18) (dual of [(524290, 2), 1048499, 19]-NRT-code), using OOA 2-folding based on linear OA(16⁸¹, 1048580, F₁₆, 18) (dual of [1048580, 1048499, 19]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸¹, 1048581, F₁₆, 18) (dual of [1048581, 1048500, 19]-code), using
- constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
  1. 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]
  2. linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(16⁹¹, 524314, F₁₆, 2, 18) (dual of [(524314, 2), 1048537, 19]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(16⁹², 524323, F₁₆, 2, 18) (dual of [(524323, 2), 1048554, 19]-NRT-code)	[i]
3	Linear OOA(16⁹³, 524328, F₁₆, 2, 18) (dual of [(524328, 2), 1048563, 19]-NRT-code)	[i]
4	Linear OOA(16⁹⁴, 524335, F₁₆, 2, 18) (dual of [(524335, 2), 1048576, 19]-NRT-code)	[i]
5	Linear OOA(16⁹⁵, 524339, F₁₆, 2, 18) (dual of [(524339, 2), 1048583, 19]-NRT-code)	[i]
6	Linear OOA(16⁹⁶, 524355, F₁₆, 2, 18) (dual of [(524355, 2), 1048614, 19]-NRT-code)	[i]
7	Digital (63, 81, 524290)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound