MinT - Information on Result #808783

Information on Result #808783

Linear OOA(2²⁰⁶, 517, F₂, 2, 42) (dual of [(517, 2), 828, 43]-NRT-code), using OOA 2-folding based on linear OA(2²⁰⁶, 1034, F₂, 42) (dual of [1034, 828, 43]-code), using

1 times truncation [i] based on linear OA(2²⁰⁷, 1035, F₂, 43) (dual of [1035, 828, 44]-code), using
- constructionÂ X applied to C_e(42) âŠ‚ C_e(40) [i] based on
  1. linear OA(2²⁰⁶, 1024, F₂, 43) (dual of [1024, 818, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
  2. 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]
  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(2²⁰⁶, 517, F₂, 3, 42) (dual of [(517, 3), 1345, 43]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁰⁶, 517, F₂, 4, 42) (dual of [(517, 4), 1862, 43]-NRT-code)	[i]
3	Linear OOA(2²⁰⁶, 517, F₂, 5, 42) (dual of [(517, 5), 2379, 43]-NRT-code)	[i]
4	Linear OOA(2²⁰⁶, 517, F₂, 6, 42) (dual of [(517, 6), 2896, 43]-NRT-code)	[i]
5	Linear OOA(2²⁰⁶, 517, F₂, 7, 42) (dual of [(517, 7), 3413, 43]-NRT-code)	[i]
6	Linear OOA(2²⁰⁶, 517, F₂, 8, 42) (dual of [(517, 8), 3930, 43]-NRT-code)	[i]
7	Digital (164, 206, 517)-net over F₂	[i]