MinT - Information on Result #2667291

Information on Result #2667291

Linear OOA(2¹³⁰, 1376, F₂, 3, 21) (dual of [(1376, 3), 3998, 22]-NRT-code), using 2² times duplication based on linear OOA(2¹²⁸, 1376, F₂, 3, 21) (dual of [(1376, 3), 4000, 22]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹²⁸, 4128, F₂, 21) (dual of [4128, 4000, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2¹²⁷, 4127, F₂, 21) (dual of [4127, 4000, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(2¹²¹, 4097, F₂, 21) (dual of [4097, 3976, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    2. linear OA(2⁹⁷, 4097, F₂, 17) (dual of [4097, 4000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    3. linear OA(2⁶, 30, F₂, 3) (dual of [30, 24, 4]-code or 30-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(2¹³⁰, 1249, F₂, 4, 21) (dual of [(1249, 4), 4866, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹³⁰, 1249, F₂, 5, 21) (dual of [(1249, 5), 6115, 22]-NRT-code)	[i]
3	Linear OOA(2¹³⁰, 1249, F₂, 6, 21) (dual of [(1249, 6), 7364, 22]-NRT-code)	[i]
4	Linear OOA(2¹³⁰, 1249, F₂, 7, 21) (dual of [(1249, 7), 8613, 22]-NRT-code)	[i]
5	Linear OOA(2¹³⁰, 1249, F₂, 8, 21) (dual of [(1249, 8), 9862, 22]-NRT-code)	[i]
6	Digital (109, 130, 1249)-net over F₂	[i]