MinT - Information on Result #807350

Information on Result #807350

Linear OOA(2¹⁴⁶, 525, F₂, 2, 28) (dual of [(525, 2), 904, 29]-NRT-code), using OOA 2-folding based on linear OA(2¹⁴⁶, 1050, F₂, 28) (dual of [1050, 904, 29]-code), using

1 times truncation [i] based on linear OA(2¹⁴⁷, 1051, F₂, 29) (dual of [1051, 904, 30]-code), using
- constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
  1. linear OA(2¹⁴¹, 1025, F₂, 29) (dual of [1025, 884, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025Â | 2²⁰âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  2. linear OA(2¹²¹, 1025, F₂, 25) (dual of [1025, 904, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025Â | 2²⁰âˆ’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, 26, F₂, 3) (dual of [26, 20, 4]-code or 26-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(2¹⁴⁶, 516, F₂, 3, 28) (dual of [(516, 3), 1402, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁴⁶, 516, F₂, 4, 28) (dual of [(516, 4), 1918, 29]-NRT-code)	[i]
3	Linear OOA(2¹⁴⁶, 516, F₂, 5, 28) (dual of [(516, 5), 2434, 29]-NRT-code)	[i]
4	Linear OOA(2¹⁴⁶, 516, F₂, 6, 28) (dual of [(516, 6), 2950, 29]-NRT-code)	[i]
5	Linear OOA(2¹⁴⁶, 516, F₂, 7, 28) (dual of [(516, 7), 3466, 29]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁶, 516, F₂, 8, 28) (dual of [(516, 8), 3982, 29]-NRT-code)	[i]
7	Digital (118, 146, 516)-net over F₂	[i]