MinT - Information on Result #1684399

Information on Result #1684399

Linear OOA(2¹⁹⁰, 1799413, F₂, 7, 15) (dual of [(1799413, 7), 12595701, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁰, 1799413, F₂, 4, 15) (dual of [(1799413, 4), 7197462, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁹⁰, 2097405, F₂, 4, 15) (dual of [(2097405, 4), 8389430, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁶, 254, F₂, 4, 7) (dual of [(254, 4), 990, 8]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
  2. linear OOA(2¹⁶⁴, 2097151, F₂, 4, 15) (dual of [(2097151, 4), 8388440, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(2¹⁶⁴, 4194302, F₂, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
      - 1 times NRT-code embedding in larger space [i] based on 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(2¹⁹⁰, 1799412, F₂, 8, 15) (dual of [(1799412, 8), 14395106, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁹⁰, 1799412, F₂, 21, 15) (dual of [(1799412, 21), 37787462, 16]-NRT-code)	[i]		OOA Stacking with Additional Row