MinT - Information on Result #806427

Information on Result #806427

Linear OOA(2¹⁰¹, 517, F₂, 2, 20) (dual of [(517, 2), 933, 21]-NRT-code), using OOA 2-folding based on linear OA(2¹⁰¹, 1034, F₂, 20) (dual of [1034, 933, 21]-code), using

1 times truncation [i] based on linear OA(2¹⁰², 1035, F₂, 21) (dual of [1035, 933, 22]-code), using
- constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
  1. 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]
  2. linear OA(2⁹¹, 1024, F₂, 19) (dual of [1024, 933, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(2¹⁰¹, 383, F₂, 3, 20) (dual of [(383, 3), 1048, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁰¹, 383, F₂, 4, 20) (dual of [(383, 4), 1431, 21]-NRT-code)	[i]
3	Linear OOA(2¹⁰¹, 383, F₂, 5, 20) (dual of [(383, 5), 1814, 21]-NRT-code)	[i]
4	Linear OOA(2¹⁰¹, 383, F₂, 6, 20) (dual of [(383, 6), 2197, 21]-NRT-code)	[i]
5	Linear OOA(2¹⁰¹, 383, F₂, 7, 20) (dual of [(383, 7), 2580, 21]-NRT-code)	[i]
6	Linear OOA(2¹⁰¹, 383, F₂, 8, 20) (dual of [(383, 8), 2963, 21]-NRT-code)	[i]
7	Digital (81, 101, 383)-net over F₂	[i]