MinT - Information on Result #2618775

Information on Result #2618775

Linear OOA(2²⁴¹, 2741, F₂, 3, 36) (dual of [(2741, 3), 7982, 37]-NRT-code), using strength reduction based on linear OOA(2²⁴¹, 2741, F₂, 3, 37) (dual of [(2741, 3), 7982, 38]-NRT-code), using

OOA 3-folding [i] based on linear OA(2²⁴¹, 8223, F₂, 37) (dual of [8223, 7982, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁴¹, 8225, F₂, 37) (dual of [8225, 7984, 38]-code), using
  - constructionÂ X applied to C([0,18]) âŠ‚ C([0,16]) [i] based on
    1. linear OA(2²³⁵, 8193, F₂, 37) (dual of [8193, 7958, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
    2. linear OA(2²⁰⁹, 8193, F₂, 33) (dual of [8193, 7984, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [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(2²⁴¹, 2171, F₂, 4, 36) (dual of [(2171, 4), 8443, 37]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁴¹, 2171, F₂, 5, 36) (dual of [(2171, 5), 10614, 37]-NRT-code)	[i]
3	Linear OOA(2²⁴¹, 2171, F₂, 6, 36) (dual of [(2171, 6), 12785, 37]-NRT-code)	[i]
4	Linear OOA(2²⁴¹, 2171, F₂, 7, 36) (dual of [(2171, 7), 14956, 37]-NRT-code)	[i]
5	Linear OOA(2²⁴¹, 2171, F₂, 8, 36) (dual of [(2171, 8), 17127, 37]-NRT-code)	[i]
6	Digital (205, 241, 2171)-net over F₂	[i]