MinT - Information on Result #1684464

Information on Result #1684464

Linear OOA(2¹⁹¹, 1928564, F₂, 7, 15) (dual of [(1928564, 7), 13499757, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹¹, 1928564, F₂, 4, 15) (dual of [(1928564, 4), 7714065, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁹¹, 2097406, F₂, 4, 15) (dual of [(2097406, 4), 8389433, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁹¹, 4194812, F₂, 2, 15) (dual of [(4194812, 2), 8389433, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2²⁹, 511, F₂, 2, 7) (dual of [(511, 2), 993, 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: 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(2¹⁹¹, 1928563, F₂, 8, 15) (dual of [(1928563, 8), 15428313, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁹¹, 1928563, F₂, 21, 15) (dual of [(1928563, 21), 40499632, 16]-NRT-code)	[i]		OOA Stacking with Additional Row