MinT - Information on Result #808689

Information on Result #808689

Linear OOA(2¹⁹⁷, 517, F₂, 2, 41) (dual of [(517, 2), 837, 42]-NRT-code), using OOA 2-folding based on linear OA(2¹⁹⁷, 1034, F₂, 41) (dual of [1034, 837, 42]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁹⁷, 1035, F₂, 41) (dual of [1035, 838, 42]-code), using
- constructionÂ X applied to C_e(40) âŠ‚ C_e(38) [i] based on
  1. linear OA(2¹⁹⁶, 1024, F₂, 41) (dual of [1024, 828, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
  2. linear OA(2¹⁸⁶, 1024, F₂, 39) (dual of [1024, 838, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
  3. linear OA(2¹, 11, F₂, 1) (dual of [11, 10, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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(2¹⁹⁷, 474, F₂, 3, 41) (dual of [(474, 3), 1225, 42]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹⁷, 474, F₂, 4, 41) (dual of [(474, 4), 1699, 42]-NRT-code)	[i]
3	Linear OOA(2¹⁹⁷, 474, F₂, 5, 41) (dual of [(474, 5), 2173, 42]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁷, 474, F₂, 6, 41) (dual of [(474, 6), 2647, 42]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁷, 474, F₂, 7, 41) (dual of [(474, 7), 3121, 42]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁷, 474, F₂, 8, 41) (dual of [(474, 8), 3595, 42]-NRT-code)	[i]
7	Digital (156, 197, 474)-net over F₂	[i]