MinT - Information on Result #806765

Information on Result #806765

Linear OOA(2¹¹², 517, F₂, 2, 23) (dual of [(517, 2), 922, 24]-NRT-code), using OOA 2-folding based on linear OA(2¹¹², 1034, F₂, 23) (dual of [1034, 922, 24]-code), using

discarding factors / shortening the dual code based on linear OA(2¹¹², 1035, F₂, 23) (dual of [1035, 923, 24]-code), using
- constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
  1. linear OA(2¹¹¹, 1024, F₂, 23) (dual of [1024, 913, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(2¹⁰¹, 1024, F₂, 21) (dual of [1024, 923, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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(2¹¹², 348, F₂, 3, 23) (dual of [(348, 3), 932, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹¹², 348, F₂, 4, 23) (dual of [(348, 4), 1280, 24]-NRT-code)	[i]
3	Linear OOA(2¹¹², 348, F₂, 5, 23) (dual of [(348, 5), 1628, 24]-NRT-code)	[i]
4	Linear OOA(2¹¹², 348, F₂, 6, 23) (dual of [(348, 6), 1976, 24]-NRT-code)	[i]
5	Linear OOA(2¹¹², 348, F₂, 7, 23) (dual of [(348, 7), 2324, 24]-NRT-code)	[i]
6	Linear OOA(2¹¹², 348, F₂, 8, 23) (dual of [(348, 8), 2672, 24]-NRT-code)	[i]
7	Digital (89, 112, 348)-net over F₂	[i]