MinT - Information on Result #1599399

Information on Result #1599399

Linear OOA(2²⁴⁵, 6595044, F₂, 4, 15) (dual of [(6595044, 4), 26379931, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁵, 6595044, F₂, 2, 15) (dual of [(6595044, 2), 13189843, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁵, large, F₂, 2, 15), using
- 2¹ times duplication [i] based on linear OOA(2²⁴⁴, large, F₂, 2, 15), using
  - 7 times NRT-code embedding in larger space [i] 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: 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(2²⁴⁵, 3297522, F₂, 7, 15) (dual of [(3297522, 7), 23082409, 16]-NRT-code)	[i]		OOA Folding