MinT - Information on Result #808619

Information on Result #808619

Linear OOA(2²⁵⁹, 2080, F₂, 2, 40) (dual of [(2080, 2), 3901, 41]-NRT-code), using OOA 2-folding based on linear OA(2²⁵⁹, 4160, F₂, 40) (dual of [4160, 3901, 41]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁵⁹, 4161, F₂, 40) (dual of [4161, 3902, 41]-code), using
- 1 times truncation [i] based on linear OA(2²⁶⁰, 4162, F₂, 41) (dual of [4162, 3902, 42]-code), using
  - constructionÂ X applied to C([0,20]) âŠ‚ C([0,16]) [i] based on
    1. linear OA(2²⁴¹, 4097, F₂, 41) (dual of [4097, 3856, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]
    2. linear OA(2¹⁹³, 4097, F₂, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
    3. linear OA(2¹⁹, 65, F₂, 7) (dual of [65, 46, 8]-code), using
      - adding a parity check bit [i] based on linear OA(2¹⁸, 64, F₂, 6) (dual of [64, 46, 7]-code), using
        extracting embedded orthogonal array [i] based on digital (12, 18, 64)-net over F₂, using
        linear code embedding found in a computer search [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(2²⁵⁹, 1753, F₂, 3, 40) (dual of [(1753, 3), 5000, 41]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁹, 1753, F₂, 4, 40) (dual of [(1753, 4), 6753, 41]-NRT-code)	[i]
3	Linear OOA(2²⁵⁹, 1753, F₂, 5, 40) (dual of [(1753, 5), 8506, 41]-NRT-code)	[i]
4	Linear OOA(2²⁵⁹, 1753, F₂, 6, 40) (dual of [(1753, 6), 10259, 41]-NRT-code)	[i]
5	Linear OOA(2²⁵⁹, 1753, F₂, 7, 40) (dual of [(1753, 7), 12012, 41]-NRT-code)	[i]
6	Linear OOA(2²⁵⁹, 1753, F₂, 8, 40) (dual of [(1753, 8), 13765, 41]-NRT-code)	[i]
7	Digital (219, 259, 1753)-net over F₂	[i]