MinT - Information on Result #856610

Information on Result #856610

Linear OOA(16⁴⁹, 2049, F₁₆, 2, 18) (dual of [(2049, 2), 4049, 19]-NRT-code), using OOA 2-folding based on linear OA(16⁴⁹, 4098, F₁₆, 18) (dual of [4098, 4049, 19]-code), using

discarding factors / shortening the dual code based on linear OA(16⁴⁹, 4099, F₁₆, 18) (dual of [4099, 4050, 19]-code), using
- constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
  1. linear OA(16⁴⁹, 4096, F₁₆, 18) (dual of [4096, 4047, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
  2. linear OA(16⁴⁶, 4096, F₁₆, 17) (dual of [4096, 4050, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  3. linear OA(16⁰, 3, F₁₆, 0) (dual of [3, 3, 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(16⁵⁸, 2066, F₁₆, 2, 18) (dual of [(2066, 2), 4074, 19]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(16⁵⁹, 2073, F₁₆, 2, 18) (dual of [(2073, 2), 4087, 19]-NRT-code)	[i]
3	Linear OOA(16⁶⁰, 2082, F₁₆, 2, 18) (dual of [(2082, 2), 4104, 19]-NRT-code)	[i]
4	Linear OOA(16⁶¹, 2087, F₁₆, 2, 18) (dual of [(2087, 2), 4113, 19]-NRT-code)	[i]
5	Linear OOA(16⁶², 2094, F₁₆, 2, 18) (dual of [(2094, 2), 4126, 19]-NRT-code)	[i]
6	Linear OOA(16⁶³, 2098, F₁₆, 2, 18) (dual of [(2098, 2), 4133, 19]-NRT-code)	[i]
7	Digital (31, 49, 2049)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound