MinT - Information on Result #3010833

Information on Result #3010833

Linear OOA(2²²³, large, F₂, 8, 12), using 2 times NRT-code embedding in larger space based on linear OOA(2²⁰⁷, large, F₂, 8, 12), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁰⁷, large, F₂, 2, 12), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2²⁰⁵, 8388602, F₂, 2, 12) (dual of [(8388602, 2), 16776999, 13]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁶⁷, 4194303, F₂, 2, 6) (dual of [(4194303, 2), 8388539, 7]-NRT-code), using
      - OOAs constructed from BCH codes [i]
    2. linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁴, large, F₂, 8, 12)	[i]		OOA Duplication
2	Linear OOA(2²²⁵, large, F₂, 8, 12)	[i]
3	Linear OOA(2²²⁶, large, F₂, 8, 12)	[i]
4	Linear OOA(2²²⁷, large, F₂, 8, 12)	[i]
5	Linear OOA(2²²⁸, large, F₂, 8, 12)	[i]
6	Linear OOA(2²²⁹, large, F₂, 8, 12)	[i]
7	Linear OOA(2²³⁰, large, F₂, 8, 12)	[i]