MinT - Information on Result #2615403

Information on Result #2615403

Linear OOA(2¹⁸⁹, 2741, F₂, 3, 28) (dual of [(2741, 3), 8034, 29]-NRT-code), using strength reduction based on linear OOA(2¹⁸⁹, 2741, F₂, 3, 29) (dual of [(2741, 3), 8034, 30]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹⁸⁹, 8223, F₂, 29) (dual of [8223, 8034, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁸⁹, 8225, F₂, 29) (dual of [8225, 8036, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(2¹⁸³, 8193, F₂, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(2¹⁵⁷, 8193, F₂, 25) (dual of [8193, 8036, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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(2¹⁸⁹, 2076, F₂, 4, 28) (dual of [(2076, 4), 8115, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸⁹, 2076, F₂, 5, 28) (dual of [(2076, 5), 10191, 29]-NRT-code)	[i]
3	Linear OOA(2¹⁸⁹, 2076, F₂, 6, 28) (dual of [(2076, 6), 12267, 29]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁹, 2076, F₂, 7, 28) (dual of [(2076, 7), 14343, 29]-NRT-code)	[i]
5	Linear OOA(2¹⁸⁹, 2076, F₂, 8, 28) (dual of [(2076, 8), 16419, 29]-NRT-code)	[i]
6	Digital (161, 189, 2076)-net over F₂	[i]