MinT - Information on Result #1515188

Information on Result #1515188

Linear OOA(2¹⁹⁹, 3857142, F₂, 3, 13) (dual of [(3857142, 3), 11571227, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁹, 3857142, F₂, 2, 13) (dual of [(3857142, 2), 7714085, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁹⁹, 4718589, F₂, 2, 13) (dual of [(4718589, 2), 9436979, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁹⁷, 4718588, F₂, 2, 13) (dual of [(4718588, 2), 9436979, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁵⁸, 524287, F₂, 2, 6) (dual of [(524287, 2), 1048516, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F₂, using
        1 times m-reduction [i] based on digital (52, 59, 524287)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
    2. linear OOA(2¹³⁹, 4194301, F₂, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹³⁹, 8388602, F₂, 13) (dual of [8388602, 8388463, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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(2¹⁹⁹, 1928571, F₂, 6, 13) (dual of [(1928571, 6), 11571227, 14]-NRT-code)	[i]		OOA Folding