MinT - Information on Result #1151568

Information on Result #1151568

Linear OOA(2²³⁰, 599194, F₂, 7, 21) (dual of [(599194, 7), 4194128, 22]-NRT-code), using OOA 7-folding based on linear OA(2²³⁰, 4194358, F₂, 21) (dual of [4194358, 4194128, 22]-code), using

2 times code embedding in larger space [i] based on linear OA(2²²⁸, 4194356, F₂, 21) (dual of [4194356, 4194128, 22]-code), using
- constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
  1. linear OA(2²²¹, 4194305, F₂, 21) (dual of [4194305, 4194084, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 2⁴⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  2. linear OA(2¹⁷⁷, 4194305, F₂, 17) (dual of [4194305, 4194128, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 2⁴⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
  3. linear OA(2⁷, 51, F₂, 3) (dual of [51, 44, 4]-code or 51-cap in PG(6,2)), using
    - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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(2²²⁹, 599193, F₂, 7, 20) (dual of [(599193, 7), 4194122, 21]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²³⁰, 599194, F₂, 8, 21) (dual of [(599194, 8), 4793322, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (209, 230, 599194)-net over F₂	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound