MinT - Information on Result #807810

Information on Result #807810

Linear OOA(2¹⁶⁶, 525, F₂, 2, 32) (dual of [(525, 2), 884, 33]-NRT-code), using OOA 2-folding based on linear OA(2¹⁶⁶, 1050, F₂, 32) (dual of [1050, 884, 33]-code), using

1 times truncation [i] based on linear OA(2¹⁶⁷, 1051, F₂, 33) (dual of [1051, 884, 34]-code), using
- constructionÂ X applied to C([0,16]) âŠ‚ C([0,14]) [i] based on
  1. linear OA(2¹⁶¹, 1025, F₂, 33) (dual of [1025, 864, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025Â | 2²⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
  2. 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]
  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(2¹⁶⁶, 525, F₂, 3, 32) (dual of [(525, 3), 1409, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶⁶, 525, F₂, 4, 32) (dual of [(525, 4), 1934, 33]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁶, 525, F₂, 5, 32) (dual of [(525, 5), 2459, 33]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁶, 525, F₂, 6, 32) (dual of [(525, 6), 2984, 33]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁶, 525, F₂, 7, 32) (dual of [(525, 7), 3509, 33]-NRT-code)	[i]
6	Linear OOA(2¹⁶⁶, 525, F₂, 8, 32) (dual of [(525, 8), 4034, 33]-NRT-code)	[i]
7	Digital (134, 166, 525)-net over F₂	[i]