MinT - Information on Result #808715

Information on Result #808715

Linear OOA(2²⁶⁰, 2081, F₂, 2, 41) (dual of [(2081, 2), 3902, 42]-NRT-code), using OOA 2-folding 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(2²⁶⁰, 1607, F₂, 3, 41) (dual of [(1607, 3), 4561, 42]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁶⁰, 1607, F₂, 4, 41) (dual of [(1607, 4), 6168, 42]-NRT-code)	[i]
3	Linear OOA(2²⁶⁰, 1607, F₂, 5, 41) (dual of [(1607, 5), 7775, 42]-NRT-code)	[i]
4	Linear OOA(2²⁶⁰, 1607, F₂, 6, 41) (dual of [(1607, 6), 9382, 42]-NRT-code)	[i]
5	Linear OOA(2²⁶⁰, 1607, F₂, 7, 41) (dual of [(1607, 7), 10989, 42]-NRT-code)	[i]
6	Linear OOA(2²⁶⁰, 1607, F₂, 8, 41) (dual of [(1607, 8), 12596, 42]-NRT-code)	[i]
7	Digital (219, 260, 1607)-net over F₂	[i]