MinT - Information on Result #2478516

Information on Result #2478516

Linear OOA(2²⁴⁸, large, F₂, 2, 15), using 9 times NRT-code embedding in larger space based on linear OOA(2²³⁰, 8388602, F₂, 2, 15) (dual of [(8388602, 2), 16776974, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁸, 4194303, F₂, 2, 7) (dual of [(4194303, 2), 8388538, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁶², 4194301, F₂, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹⁶², 8388602, F₂, 15) (dual of [8388602, 8388440, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and 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		Method
1	Linear OOA(2²⁴⁹, large, F₂, 2, 15)	[i]	OOA Duplication
2	Linear OOA(2²⁴⁸, 7842877, F₂, 3, 15) (dual of [(7842877, 3), 23528383, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2²⁴⁸, 7842877, F₂, 4, 15) (dual of [(7842877, 4), 31371260, 16]-NRT-code)	[i]
4	Linear OOA(2²⁴⁸, 7842877, F₂, 5, 15) (dual of [(7842877, 5), 39214137, 16]-NRT-code)	[i]
5	Linear OOA(2²⁴⁸, 7842877, F₂, 6, 15) (dual of [(7842877, 6), 47057014, 16]-NRT-code)	[i]
6	Linear OOA(2²⁴⁸, 7842877, F₂, 7, 15) (dual of [(7842877, 7), 54899891, 16]-NRT-code)	[i]
7	Linear OOA(2²⁴⁸, 7842877, F₂, 8, 15) (dual of [(7842877, 8), 62742768, 16]-NRT-code)	[i]
8	Digital (233, 248, 7842877)-net over F₂	[i]