MinT - Information on Result #809189

Information on Result #809189

Linear OOA(2²⁵⁹, 1037, F₂, 2, 46) (dual of [(1037, 2), 1815, 47]-NRT-code), using OOA 2-folding based on linear OA(2²⁵⁹, 2074, F₂, 46) (dual of [2074, 1815, 47]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁵⁹, 2075, F₂, 46) (dual of [2075, 1816, 47]-code), using
- 1 times truncation [i] based on linear OA(2²⁶⁰, 2076, F₂, 47) (dual of [2076, 1816, 48]-code), using
  - constructionÂ X applied to C_e(46) âŠ‚ C_e(42) [i] based on
    1. linear OA(2²⁵⁴, 2048, F₂, 47) (dual of [2048, 1794, 48]-code), using an extension C_e(46) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,46], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 47 [i]
    2. linear OA(2²³², 2048, F₂, 43) (dual of [2048, 1816, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
    3. linear OA(2⁶, 28, F₂, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
      - discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [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(2²⁵⁹, 1002, F₂, 3, 46) (dual of [(1002, 3), 2747, 47]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁹, 1002, F₂, 4, 46) (dual of [(1002, 4), 3749, 47]-NRT-code)	[i]
3	Linear OOA(2²⁵⁹, 1002, F₂, 5, 46) (dual of [(1002, 5), 4751, 47]-NRT-code)	[i]
4	Linear OOA(2²⁵⁹, 1002, F₂, 6, 46) (dual of [(1002, 6), 5753, 47]-NRT-code)	[i]
5	Linear OOA(2²⁵⁹, 1002, F₂, 7, 46) (dual of [(1002, 7), 6755, 47]-NRT-code)	[i]
6	Linear OOA(2²⁵⁹, 1002, F₂, 8, 46) (dual of [(1002, 8), 7757, 47]-NRT-code)	[i]
7	Digital (213, 259, 1002)-net over F₂	[i]