MinT - Information on Result #806885

Information on Result #806885

Linear OOA(2¹²⁶, 525, F₂, 2, 24) (dual of [(525, 2), 924, 25]-NRT-code), using OOA 2-folding based on linear OA(2¹²⁶, 1050, F₂, 24) (dual of [1050, 924, 25]-code), using

1 times truncation [i] based on linear OA(2¹²⁷, 1051, F₂, 25) (dual of [1051, 924, 26]-code), using
- constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
  1. 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]
  2. linear OA(2¹⁰¹, 1025, F₂, 21) (dual of [1025, 924, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025Â | 2²⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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(2¹²⁶, 490, F₂, 3, 24) (dual of [(490, 3), 1344, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹²⁶, 490, F₂, 4, 24) (dual of [(490, 4), 1834, 25]-NRT-code)	[i]
3	Linear OOA(2¹²⁶, 490, F₂, 5, 24) (dual of [(490, 5), 2324, 25]-NRT-code)	[i]
4	Linear OOA(2¹²⁶, 490, F₂, 6, 24) (dual of [(490, 6), 2814, 25]-NRT-code)	[i]
5	Linear OOA(2¹²⁶, 490, F₂, 7, 24) (dual of [(490, 7), 3304, 25]-NRT-code)	[i]
6	Linear OOA(2¹²⁶, 490, F₂, 8, 24) (dual of [(490, 8), 3794, 25]-NRT-code)	[i]
7	Digital (102, 126, 490)-net over F₂	[i]