MinT - Information on Result #2425767

Information on Result #2425767

Linear OOA(2²¹⁸, 4456444, F₂, 2, 14) (dual of [(4456444, 2), 8912670, 15]-NRT-code), using strength reduction based on linear OOA(2²¹⁸, 4456444, F₂, 2, 15) (dual of [(4456444, 2), 8912670, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵⁶, 262143, F₂, 2, 7) (dual of [(262143, 2), 524230, 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 s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²¹⁸, 4000801, F₂, 3, 14) (dual of [(4000801, 3), 12002185, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁸, 4000801, F₂, 4, 14) (dual of [(4000801, 4), 16002986, 15]-NRT-code)	[i]
3	Linear OOA(2²¹⁸, 4000801, F₂, 5, 14) (dual of [(4000801, 5), 20003787, 15]-NRT-code)	[i]
4	Linear OOA(2²¹⁸, 4000801, F₂, 6, 14) (dual of [(4000801, 6), 24004588, 15]-NRT-code)	[i]
5	Linear OOA(2²¹⁸, 4000801, F₂, 7, 14) (dual of [(4000801, 7), 28005389, 15]-NRT-code)	[i]
6	Linear OOA(2²¹⁸, 4000801, F₂, 8, 14) (dual of [(4000801, 8), 32006190, 15]-NRT-code)	[i]
7	Digital (204, 218, 4000801)-net over F₂	[i]