MinT - Information on Result #1692688

Information on Result #1692688

Linear OOA(2¹⁰⁴, 3604519, F₂, 8, 8) (dual of [(3604519, 8), 28836048, 9]-NRT-code), using appending kth column based on linear OOA(2¹⁰⁴, 3604519, F₂, 7, 8) (dual of [(3604519, 7), 25231529, 9]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁰⁴, 3604519, F₂, 2, 8) (dual of [(3604519, 2), 7208934, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁰⁴, 4194366, F₂, 2, 8) (dual of [(4194366, 2), 8388628, 9]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹², 65, F₂, 2, 4) (dual of [(65, 2), 118, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (8, 12, 65)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
    2. linear OOA(2⁹², 4194301, F₂, 2, 8) (dual of [(4194301, 2), 8388510, 9]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2⁹², 8388602, F₂, 8) (dual of [8388602, 8388510, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(2⁹², large, F₂, 8) (dual of [large, large−92, 9]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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	Digital (96, 104, 3604519)-net over F₂	[i]		Net Defined by OOA