MinT - Information on Result #2616179

Information on Result #2616179

Linear OOA(2²⁰², 2741, F₂, 3, 30) (dual of [(2741, 3), 8021, 31]-NRT-code), using strength reduction based on linear OOA(2²⁰², 2741, F₂, 3, 31) (dual of [(2741, 3), 8021, 32]-NRT-code), using

OOA 3-folding [i] based on linear OA(2²⁰², 8223, F₂, 31) (dual of [8223, 8021, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁰², 8224, F₂, 31) (dual of [8224, 8022, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
    1. 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]
    2. linear OA(2¹⁷⁰, 8192, F₂, 27) (dual of [8192, 8022, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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(2²⁰², 2087, F₂, 4, 30) (dual of [(2087, 4), 8146, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁰², 2087, F₂, 5, 30) (dual of [(2087, 5), 10233, 31]-NRT-code)	[i]
3	Linear OOA(2²⁰², 2087, F₂, 6, 30) (dual of [(2087, 6), 12320, 31]-NRT-code)	[i]
4	Linear OOA(2²⁰², 2087, F₂, 7, 30) (dual of [(2087, 7), 14407, 31]-NRT-code)	[i]
5	Linear OOA(2²⁰², 2087, F₂, 8, 30) (dual of [(2087, 8), 16494, 31]-NRT-code)	[i]
6	Digital (172, 202, 2087)-net over F₂	[i]