MinT - Information on Result #2668731

Information on Result #2668731

Linear OOA(2²³³, 2743, F₂, 3, 35) (dual of [(2743, 3), 7996, 36]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²³⁰, 2742, F₂, 3, 35) (dual of [(2742, 3), 7996, 36]-NRT-code), using

OOA 3-folding [i] based on linear OA(2²³⁰, 8226, F₂, 35) (dual of [8226, 7996, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2²²⁸, 8224, F₂, 35) (dual of [8224, 7996, 36]-code), using
  - constructionÂ X applied to C_e(34) âŠ‚ C_e(30) [i] based on
    1. linear OA(2²²², 8192, F₂, 35) (dual of [8192, 7970, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    2. linear OA(2¹⁹⁶, 8192, F₂, 31) (dual of [8192, 7996, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    3. 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(2²³³, 2081, F₂, 4, 35) (dual of [(2081, 4), 8091, 36]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³³, 2081, F₂, 5, 35) (dual of [(2081, 5), 10172, 36]-NRT-code)	[i]
3	Linear OOA(2²³³, 2081, F₂, 6, 35) (dual of [(2081, 6), 12253, 36]-NRT-code)	[i]
4	Linear OOA(2²³³, 2081, F₂, 7, 35) (dual of [(2081, 7), 14334, 36]-NRT-code)	[i]
5	Linear OOA(2²³³, 2081, F₂, 8, 35) (dual of [(2081, 8), 16415, 36]-NRT-code)	[i]
6	Digital (198, 233, 2081)-net over F₂	[i]