MinT - Information on Result #1685906

Information on Result #1685906

Linear OOA(2²¹¹, 2416657, F₂, 7, 15) (dual of [(2416657, 7), 16916388, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹¹, 2416657, F₂, 3, 15) (dual of [(2416657, 3), 7249760, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹¹, 2828968, F₂, 3, 15) (dual of [(2828968, 3), 8486693, 16]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2²⁰⁹, 2828968, F₂, 3, 15) (dual of [(2828968, 3), 8486695, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁴⁷, 32767, F₂, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
    2. linear OOA(2¹⁶², 2796201, F₂, 3, 15) (dual of [(2796201, 3), 8388441, 16]-NRT-code), using
      - OOA 3-folding [i] 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: 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		This result only	Method
1	Linear OOA(2²¹¹, 2416656, F₂, 8, 15) (dual of [(2416656, 8), 19333037, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2²¹¹, 2416656, F₂, 21, 15) (dual of [(2416656, 21), 50749565, 16]-NRT-code)	[i]		OOA Stacking with Additional Row