MinT - Information on Result #1053447

Information on Result #1053447

Linear OOA(2²¹⁰, 4109, F₂, 4, 29) (dual of [(4109, 4), 16226, 30]-NRT-code), using OOA 4-folding based on linear OA(2²¹⁰, 16436, F₂, 29) (dual of [16436, 16226, 30]-code), using

discarding factors / shortening the dual code based on linear OA(2²¹⁰, 16439, F₂, 29) (dual of [16439, 16229, 30]-code), using
- constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
  1. linear OA(2¹⁹⁷, 16384, F₂, 29) (dual of [16384, 16187, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
  2. linear OA(2¹⁵⁵, 16384, F₂, 23) (dual of [16384, 16229, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  3. linear OA(2¹³, 55, F₂, 5) (dual of [55, 42, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³, 63, F₂, 5) (dual of [63, 50, 6]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(2²¹⁰, 3725, F₂, 5, 29) (dual of [(3725, 5), 18415, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁰, 3725, F₂, 6, 29) (dual of [(3725, 6), 22140, 30]-NRT-code)	[i]
3	Linear OOA(2²¹⁰, 3725, F₂, 7, 29) (dual of [(3725, 7), 25865, 30]-NRT-code)	[i]
4	Linear OOA(2²¹⁰, 3725, F₂, 8, 29) (dual of [(3725, 8), 29590, 30]-NRT-code)	[i]
5	Digital (181, 210, 3725)-net over F₂	[i]